177種216階群

陳松良的《關于216階群的完全分類》一文證明G216共有177種互不同構的類型,并獲得了G的全部構造。

gap> NumberSmallGroups(216);

177

gap> for n in [1..177] do G:=SmallGroup(216,n);idn:=IdGroup(G);Print(idn);Print(":");L:=List(Elements(G),Order);;M:=[1,2,3,4,6,8,12,18,27,36,54,72,108,216];;for i in M do Print(Size(Positions(L,i)),","); od;Print("\n");od;                 

[ 216, 1 ]:1,1,2,2,2,108,4,6,18,12,18,0,36,0,

[ 216, 2 ]:1,1,2,2,2,4,4,6,18,12,18,24,36,72,

[ 216, 3 ]:1,1,2,6,2,0,12,6,72,36,72,0,0,0,

[ 216, 4 ]:1,1,2,110,2,0,4,6,18,12,18,0,36,0,

[ 216, 5 ]:1,55,2,56,2,0,4,6,18,12,18,0,36,0,

[ 216, 6 ]:1,109,2,2,2,0,4,6,18,12,18,0,36,0,

[ 216, 7 ]:1,3,2,108,6,0,0,18,18,0,54,0,0,0,

[ 216, 8 ]:1,57,2,54,6,0,0,18,18,0,54,0,0,0,

[ 216, 9 ]:1,3,2,4,6,0,8,18,18,24,54,0,72,0,

[ 216, 10 ]:1,5,2,2,10,0,4,30,18,12,90,0,36,0,

[ 216, 11 ]:1,1,2,6,2,0,12,6,18,36,18,0,108,0,

[ 216, 12 ]:1,1,8,2,8,36,16,18,0,36,0,0,0,0,

[ 216, 13 ]:1,1,8,2,8,12,16,18,0,36,0,72,0,0,

[ 216, 14 ]:1,1,26,2,26,36,52,0,0,0,0,0,0,0,

[ 216, 15 ]:1,1,8,2,8,36,16,18,0,36,0,0,0,0,

[ 216, 16 ]:1,1,8,2,8,108,16,18,0,36,0,0,0,0,

[ 216, 17 ]:1,1,26,2,26,36,52,0,0,0,0,0,0,0,

[ 216, 18 ]:1,1,8,2,8,4,16,18,0,36,0,72,0,0,

[ 216, 19 ]:1,1,26,2,26,4,52,0,0,0,0,0,0,0,

[ 216, 20 ]:1,1,8,2,8,4,16,18,0,36,0,72,0,0,

[ 216, 21 ]:1,57,2,54,6,0,0,18,72,0,0,0,0,0,

[ 216, 22 ]:1,7,2,0,14,0,0,42,72,0,72,0,0,0,

[ 216, 23 ]:1,111,2,0,6,0,0,18,18,0,54,0,0,0,

[ 216, 24 ]:1,7,2,0,14,0,0,42,18,0,126,0,0,0,

[ 216, 25 ]:1,1,26,18,26,36,36,0,0,0,0,0,0,0,

[ 216, 26 ]:1,1,8,78,8,0,48,18,0,36,0,0,0,0,

[ 216, 27 ]:1,19,8,60,44,0,12,18,0,36,0,0,0,0,

[ 216, 28 ]:1,55,8,24,8,0,48,18,0,36,0,0,0,0,

[ 216, 29 ]:1,73,8,6,44,0,12,18,0,36,0,0,0,0,

[ 216, 30 ]:1,7,8,72,20,0,36,54,0,0,0,0,0,0,

[ 216, 31 ]:1,25,8,54,56,0,0,54,0,0,0,0,0,0,

[ 216, 32 ]:1,61,8,18,20,0,36,54,0,0,0,0,0,0,

[ 216, 33 ]:1,1,26,54,26,0,108,0,0,0,0,0,0,0,

[ 216, 34 ]:1,19,26,36,62,0,72,0,0,0,0,0,0,0,

[ 216, 35 ]:1,37,26,18,98,0,36,0,0,0,0,0,0,0,

[ 216, 36 ]:1,19,26,36,62,0,72,0,0,0,0,0,0,0,

[ 216, 37 ]:1,37,26,18,98,0,36,0,0,0,0,0,0,0,

[ 216, 38 ]:1,1,26,6,26,0,12,54,0,36,0,0,0,0,

[ 216, 39 ]:1,1,26,6,26,0,12,54,0,36,0,0,0,0,

[ 216, 40 ]:1,1,8,6,8,0,48,72,0,0,0,0,0,0,

[ 216, 41 ]:1,1,8,6,8,0,48,72,0,0,0,0,0,0,

[ 216, 42 ]:1,1,80,6,80,0,48,0,0,0,0,0,0,0,

[ 216, 43 ]:1,1,8,38,8,0,88,18,0,36,0,0,0,0,

[ 216, 44 ]:1,1,8,14,8,0,40,18,0,108,0,0,0,0,

[ 216, 45 ]:1,19,8,20,44,0,52,18,0,36,0,0,0,0,

[ 216, 46 ]:1,37,8,2,80,0,16,18,0,36,0,0,0,0,

[ 216, 47 ]:1,7,8,8,20,0,28,54,0,72,0,0,0,0,

[ 216, 48 ]:1,13,8,2,32,0,16,90,0,36,0,0,0,0,

[ 216, 49 ]:1,1,26,38,26,0,124,0,0,0,0,0,0,0,

[ 216, 50 ]:1,19,26,20,62,0,88,0,0,0,0,0,0,0,

[ 216, 51 ]:1,37,26,2,98,0,52,0,0,0,0,0,0,0,

[ 216, 52 ]:1,1,8,38,8,0,88,18,0,36,0,0,0,0,

[ 216, 53 ]:1,19,8,20,44,0,52,18,0,36,0,0,0,0,

[ 216, 54 ]:1,37,8,2,80,0,16,18,0,36,0,0,0,0,

[ 216, 55 ]:1,3,8,36,24,0,72,54,0,0,0,0,0,0,

[ 216, 56 ]:1,3,8,12,24,0,24,54,0,72,0,0,0,0,

[ 216, 57 ]:1,21,8,18,60,0,36,54,0,0,0,0,0,0,

[ 216, 58 ]:1,9,8,6,36,0,12,90,0,36,0,0,0,0,

[ 216, 59 ]:1,3,26,36,78,0,72,0,0,0,0,0,0,0,

[ 216, 60 ]:1,21,26,18,114,0,36,0,0,0,0,0,0,0,

[ 216, 61 ]:1,3,8,36,24,0,72,54,0,0,0,0,0,0,

[ 216, 62 ]:1,21,8,18,60,0,36,54,0,0,0,0,0,0,

[ 216, 63 ]:1,1,8,110,8,0,16,18,0,36,0,0,0,0,

[ 216, 64 ]:1,55,8,56,8,0,16,18,0,36,0,0,0,0,

[ 216, 65 ]:1,109,8,2,8,0,16,18,0,36,0,0,0,0,

[ 216, 66 ]:1,1,26,38,26,0,124,0,0,0,0,0,0,0,

[ 216, 67 ]:1,19,26,20,62,0,88,0,0,0,0,0,0,0,

[ 216, 68 ]:1,37,26,2,98,0,52,0,0,0,0,0,0,0,

[ 216, 69 ]:1,3,8,108,24,0,0,54,0,0,0,0,0,0,

[ 216, 70 ]:1,57,8,54,24,0,0,54,0,0,0,0,0,0,

[ 216, 71 ]:1,3,26,36,78,0,72,0,0,0,0,0,0,0,

[ 216, 72 ]:1,21,26,18,114,0,36,0,0,0,0,0,0,0,

[ 216, 73 ]:1,3,8,4,24,0,32,54,0,72,0,0,0,0,

[ 216, 74 ]:1,3,26,4,78,0,104,0,0,0,0,0,0,0,

[ 216, 75 ]:1,3,8,4,24,0,32,54,0,72,0,0,0,0,

[ 216, 76 ]:1,5,8,2,40,0,16,90,0,36,0,0,0,0,

[ 216, 77 ]:1,5,26,2,130,0,52,0,0,0,0,0,0,0,

[ 216, 78 ]:1,5,8,2,40,0,16,90,0,36,0,0,0,0,

[ 216, 79 ]:1,1,8,6,8,0,48,18,0,108,0,0,0,0,

[ 216, 80 ]:1,1,26,6,26,0,156,0,0,0,0,0,0,0,

[ 216, 81 ]:1,1,8,6,8,0,48,18,0,108,0,0,0,0,

[ 216, 82 ]:1,1,26,2,26,12,52,0,0,0,0,0,0,0,

[ 216, 83 ]:1,1,26,2,26,36,52,0,0,0,0,0,0,0,

[ 216, 84 ]:1,1,26,2,26,108,52,0,0,0,0,0,0,0,

[ 216, 85 ]:1,1,26,2,26,4,52,0,0,0,0,0,0,0,

[ 216, 86 ]:1,9,26,18,18,108,36,0,0,0,0,0,0,0,

[ 216, 87 ]:1,45,26,18,90,0,36,0,0,0,0,0,0,0,

[ 216, 88 ]:1,9,26,54,18,0,108,0,0,0,0,0,0,0,

[ 216, 89 ]:1,9,26,6,18,0,12,54,0,36,0,0,0,0,

[ 216, 90 ]:1,21,8,18,60,0,36,0,0,0,0,0,0,0,

[ 216, 91 ]:1,21,8,18,60,0,36,0,0,0,0,0,0,0,

[ 216, 92 ]:1,21,80,18,60,0,36,0,0,0,0,0,0,0,

[ 216, 93 ]:1,57,26,54,6,0,0,18,0,0,0,0,0,0,

[ 216, 94 ]:1,57,8,54,24,0,0,0,0,0,0,0,0,0,

[ 216, 95 ]:1,21,80,18,60,0,36,0,0,0,0,0,0,0,

[ 216, 96 ]:1,39,26,0,78,0,0,18,0,0,0,0,0,0,

[ 216, 97 ]:1,39,26,0,78,0,0,18,0,0,0,0,0,0,

[ 216, 98 ]:1,15,8,0,48,0,0,72,0,0,0,0,0,0,

[ 216, 99 ]:1,39,80,0,96,0,0,0,0,0,0,0,0,0,

[ 216, 100 ]:1,19,26,36,62,0,72,0,0,0,0,0,0,0,

[ 216, 101 ]:1,79,8,0,56,0,0,54,0,0,0,0,0,0,

[ 216, 102 ]:1,55,26,0,134,0,0,0,0,0,0,0,0,0,

[ 216, 103 ]:1,7,26,0,38,0,0,90,0,0,0,0,0,0,

[ 216, 104 ]:1,7,26,0,38,0,0,90,0,0,0,0,0,0,

[ 216, 105 ]:1,7,8,0,56,0,0,72,0,0,0,0,0,0,

[ 216, 106 ]:1,7,8,0,56,0,0,72,0,0,0,0,0,0,

[ 216, 107 ]:1,7,80,0,128,0,0,0,0,0,0,0,0,0,

[ 216, 108 ]:1,39,8,0,96,0,0,54,0,0,0,0,0,0,

[ 216, 109 ]:1,15,8,0,48,0,0,126,0,0,0,0,0,0,

[ 216, 110 ]:1,39,26,0,150,0,0,0,0,0,0,0,0,0,

[ 216, 111 ]:1,39,8,0,96,0,0,54,0,0,0,0,0,0,

[ 216, 112 ]:1,111,8,0,24,0,0,54,0,0,0,0,0,0,

[ 216, 113 ]:1,39,26,0,150,0,0,0,0,0,0,0,0,0,

[ 216, 114 ]:1,7,8,0,56,0,0,126,0,0,0,0,0,0,

[ 216, 115 ]:1,7,26,0,182,0,0,0,0,0,0,0,0,0,

[ 216, 116 ]:1,7,8,0,56,0,0,126,0,0,0,0,0,0,

[ 216, 117 ]:1,1,26,18,26,36,36,0,0,0,0,0,0,0,

[ 216, 118 ]:1,1,26,18,26,108,36,0,0,0,0,0,0,0,

[ 216, 119 ]:1,7,26,24,74,0,84,0,0,0,0,0,0,0,

[ 216, 120 ]:1,19,26,12,62,0,96,0,0,0,0,0,0,0,

[ 216, 121 ]:1,13,26,18,122,0,36,0,0,0,0,0,0,0,

[ 216, 122 ]:1,25,26,6,110,0,48,0,0,0,0,0,0,0,

[ 216, 123 ]:1,1,26,30,26,0,132,0,0,0,0,0,0,0,

[ 216, 124 ]:1,7,26,72,74,0,36,0,0,0,0,0,0,0,

[ 216, 125 ]:1,19,26,60,62,0,48,0,0,0,0,0,0,0,

[ 216, 126 ]:1,55,26,24,26,0,84,0,0,0,0,0,0,0,

[ 216, 127 ]:1,25,26,54,110,0,0,0,0,0,0,0,0,0,

[ 216, 128 ]:1,61,26,18,74,0,36,0,0,0,0,0,0,0,

[ 216, 129 ]:1,73,26,6,62,0,48,0,0,0,0,0,0,0,

[ 216, 130 ]:1,1,26,78,26,0,84,0,0,0,0,0,0,0,

[ 216, 131 ]:1,19,26,36,62,0,72,0,0,0,0,0,0,0,

[ 216, 132 ]:1,37,26,18,98,0,36,0,0,0,0,0,0,0,

[ 216, 133 ]:1,1,26,54,26,0,108,0,0,0,0,0,0,0,

[ 216, 134 ]:1,1,80,6,80,0,48,0,0,0,0,0,0,0,

[ 216, 135 ]:1,1,26,14,26,0,148,0,0,0,0,0,0,0,

[ 216, 136 ]:1,7,26,8,74,0,100,0,0,0,0,0,0,0,

[ 216, 137 ]:1,13,26,2,122,0,52,0,0,0,0,0,0,0,

[ 216, 138 ]:1,3,26,12,78,0,96,0,0,0,0,0,0,0,

[ 216, 139 ]:1,9,26,6,126,0,48,0,0,0,0,0,0,0,

[ 216, 140 ]:1,1,26,38,26,0,124,0,0,0,0,0,0,0,

[ 216, 141 ]:1,19,26,20,62,0,88,0,0,0,0,0,0,0,

[ 216, 142 ]:1,37,26,2,98,0,52,0,0,0,0,0,0,0,

[ 216, 143 ]:1,3,26,36,78,0,72,0,0,0,0,0,0,0,

[ 216, 144 ]:1,21,26,18,114,0,36,0,0,0,0,0,0,0,

[ 216, 145 ]:1,1,26,110,26,0,52,0,0,0,0,0,0,0,

[ 216, 146 ]:1,55,26,56,26,0,52,0,0,0,0,0,0,0,

[ 216, 147 ]:1,109,26,2,26,0,52,0,0,0,0,0,0,0,

[ 216, 148 ]:1,3,26,108,78,0,0,0,0,0,0,0,0,0,

[ 216, 149 ]:1,57,26,54,78,0,0,0,0,0,0,0,0,0,

[ 216, 150 ]:1,3,26,4,78,0,104,0,0,0,0,0,0,0,

[ 216, 151 ]:1,5,26,2,130,0,52,0,0,0,0,0,0,0,

[ 216, 152 ]:1,1,26,6,26,0,156,0,0,0,0,0,0,0,

[ 216, 153 ]:1,9,80,54,72,0,0,0,0,0,0,0,0,0,

[ 216, 154 ]:1,9,26,18,18,36,36,0,0,0,0,0,0,0,

[ 216, 155 ]:1,9,26,18,18,108,36,0,0,0,0,0,0,0,

[ 216, 156 ]:1,39,26,72,42,0,36,0,0,0,0,0,0,0,

[ 216, 157 ]:1,21,26,18,114,0,36,0,0,0,0,0,0,0,

[ 216, 158 ]:1,33,26,54,102,0,0,0,0,0,0,0,0,0,

[ 216, 159 ]:1,45,26,18,90,0,36,0,0,0,0,0,0,0,

[ 216, 160 ]:1,9,26,54,18,0,108,0,0,0,0,0,0,0,

[ 216, 161 ]:1,9,26,126,18,0,36,0,0,0,0,0,0,0,

[ 216, 162 ]:1,63,26,0,126,0,0,0,0,0,0,0,0,0,

[ 216, 163 ]:1,9,80,6,72,0,48,0,0,0,0,0,0,0,

[ 216, 164 ]:1,21,80,18,60,0,36,0,0,0,0,0,0,0,

[ 216, 165 ]:1,57,80,54,24,0,0,0,0,0,0,0,0,0,

[ 216, 166 ]:1,15,80,0,120,0,0,0,0,0,0,0,0,0,

[ 216, 167 ]:1,39,80,0,96,0,0,0,0,0,0,0,0,0,

[ 216, 168 ]:1,19,26,36,62,0,72,0,0,0,0,0,0,0,

[ 216, 169 ]:1,19,26,108,62,0,0,0,0,0,0,0,0,0,

[ 216, 170 ]:1,31,26,0,158,0,0,0,0,0,0,0,0,0,

[ 216, 171 ]:1,79,26,0,110,0,0,0,0,0,0,0,0,0,

[ 216, 172 ]:1,55,26,0,134,0,0,0,0,0,0,0,0,0,

[ 216, 173 ]:1,7,80,0,128,0,0,0,0,0,0,0,0,0,

[ 216, 174 ]:1,15,26,0,174,0,0,0,0,0,0,0,0,0,

[ 216, 175 ]:1,39,26,0,150,0,0,0,0,0,0,0,0,0,

[ 216, 176 ]:1,111,26,0,78,0,0,0,0,0,0,0,0,0,

[ 216, 177 ]:1,7,26,0,182,0,0,0,0,0,0,0,0,0,

gap> for n in [1..177] do G:=SmallGroup(216,n);idn:=IdGroup(G);Print(idn);Print(":");L:=List(Elements(G),Order);;M:=[1,2,3,4,6,8,12,18,27,36,54,72,108,216];;for i in M do Print(Size(Positions(L,i)),","); od;arr:=[];;idn:=IdGroup(G);cl:=ConjugacyClasses(G);;Append(arr,"共轭類數：");;Append(arr,String(Size(cl)));Append(arr,"中心：");;Append(arr,String(IdGroup(Center(G))));;Append(arr,"換位子群：");;Append(arr,String(IdGroup(DerivedSubgroup(G))));;Append(arr,"自同構群：");;Append(arr,String(Order(AutomorphismGroup(G))));;cl:=NormalSubgroups(G);;Append(arr,"正規子群個數：");;len:=Size(cl);;Append(arr,String(len));;Print(arr);Print("\n");od;

[ 216, 1 ]:1,1,2,2,2,108,4,6,18,12,18,0,36,

0,共轭類數：60中心：[ 4, 1 ]換位子群：[ 27, 1 ]自同構群：1944正規子群個數：13

[ 216, 2 ]:1,1,2,2,2,4,4,6,18,12,18,24,36,

72,共轭類數：216中心：[ 216, 2 ]換位子群：[ 1, 1 ]自同構群：72正規子群個數：16

[ 216, 3 ]:1,1,2,6,2,0,12,6,72,36,72,0,0,

0,共轭類數：63中心：[ 18, 2 ]換位子群：[ 8, 4 ]自同構群：216正規子群個數：10

[ 216, 4 ]:1,1,2,110,2,0,4,6,18,12,18,0,36,

0,共轭類數：57中心：[ 2, 1 ]換位子群：[ 54, 2 ]自同構群：3888正規子群個數：15

[ 216, 5 ]:1,55,2,56,2,0,4,6,18,12,18,0,36,

0,共轭類數：60中心：[ 4, 1 ]換位子群：[ 27, 1 ]自同構群：1944正規子群個數：17

[ 216, 6 ]:1,109,2,2,2,0,4,6,18,12,18,0,36,

0,共轭類數：57中心：[ 2, 1 ]換位子群：[ 54, 2 ]自同構群：3888正規子群個數：15

[ 216, 7 ]:1,3,2,108,6,0,0,18,18,0,54,0,0,

0,共轭類數：60中心：[ 4, 2 ]換位子群：[ 27, 1 ]自同構群：3888正規子群個數：23

[ 216, 8 ]:1,57,2,54,6,0,0,18,18,0,54,0,0,

0,共轭類數：57中心：[ 2, 1 ]換位子群：[ 54, 2 ]自同構群：1944正規子群個數：15

[ 216, 9 ]:1,3,2,4,6,0,8,18,18,24,54,0,72,

0,共轭類數：216中心：[ 216, 9 ]換位子群：[ 1, 1 ]自同構群：144正規子群個數：32

[ 216, 10 ]:1,5,2,2,10,0,4,30,18,12,90,0,36,

0,共轭類數：135中心：[ 54, 2 ]換位子群：[ 2, 1 ]自同構群：144正規子群個數：24

[ 216, 11 ]:1,1,2,6,2,0,12,6,18,36,18,0,108,

0,共轭類數：135中心：[ 54, 2 ]換位子群：[ 2, 1 ]自同構群：432正規子群個數：24

[ 216, 12 ]:1,1,8,2,8,36,16,18,0,36,0,0,0,

0,共轭類數：72中心：[ 12, 2 ]換位子群：[ 9, 1 ]自同構群：432正規子群個數：20

[ 216, 13 ]:1,1,8,2,8,12,16,18,0,36,0,72,0,

0,共轭類數：108中心：[ 36, 2 ]換位子群：[ 3, 1 ]自同構群：144正規子群個數：21

[ 216, 14 ]:1,1,26,2,26,36,52,0,0,0,0,0,0,

0,共轭類數：40中心：[ 4, 1 ]換位子群：[ 9, 2 ]自同構群：432正規子群個數：17

[ 216, 15 ]:1,1,8,2,8,36,16,18,0,36,0,0,0,

0,共轭類數：40中心：[ 4, 1 ]換位子群：[ 9, 1 ]自同構群：216正規子群個數：17

[ 216, 16 ]:1,1,8,2,8,108,16,18,0,36,0,0,0,

0,共轭類數：60中心：[ 4, 1 ]換位子群：[ 27, 2 ]自同構群：11664正規子群個數：31

[ 216, 17 ]:1,1,26,2,26,36,52,0,0,0,0,0,0,

0,共轭類數：40中心：[ 12, 2 ]換位子群：[ 27, 3 ]自同構群：1728正規子群個數：22

[ 216, 18 ]:1,1,8,2,8,4,16,18,0,36,0,72,0,

0,共轭類數：216中心：[ 216, 18 ]換位子群：[ 1, 1 ]自同構群：432正規子群個數：40

[ 216, 19 ]:1,1,26,2,26,4,52,0,0,0,0,0,0,

0,共轭類數：88中心：[ 24, 2 ]換位子群：[ 3, 1 ]自同構群：1728正規子群個數：28

[ 216, 20 ]:1,1,8,2,8,4,16,18,0,36,0,72,0,

0,共轭類數：88中心：[ 24, 2 ]換位子群：[ 3, 1 ]自同構群：216正規子群個數：28

[ 216, 21 ]:1,57,2,54,6,0,0,18,72,0,0,0,0,

0,共轭類數：21中心：[ 1, 1 ]換位子群：[ 108, 3 ]自同構群：1944正規子群個數：8

[ 216, 22 ]:1,7,2,0,14,0,0,42,72,0,72,0,0,

0,共轭類數：72中心：[ 18, 2 ]換位子群：[ 4, 2 ]自同構群：216正規子群個數：14

[ 216, 23 ]:1,111,2,0,6,0,0,18,18,0,54,0,0,

0,共轭類數：60中心：[ 4, 2 ]換位子群：[ 27, 1 ]自同構群：11664正規子群個數：31

[ 216, 24 ]:1,7,2,0,14,0,0,42,18,0,126,0,0,

0,共轭類數：216中心：[ 216, 24 ]換位子群：[ 1, 1 ]自同構群：3024正規子群個數：64

[ 216, 25 ]:1,1,26,18,26,36,36,0,0,0,0,0,0,

0,共轭類數：28中心：[ 6, 2 ]換位子群：[ 27, 3 ]自同構群：288正規子群個數：8

[ 216, 26 ]:1,1,8,78,8,0,48,18,0,36,0,0,0,

0,共轭類數：33中心：[ 2, 1 ]換位子群：[ 54, 9 ]自同構群：1296正規子群個數：19

[ 216, 27 ]:1,19,8,60,44,0,12,18,0,36,0,0,0,

0,共轭類數：36中心：[ 2, 1 ]換位子群：[ 27, 2 ]自同構群：1296正規子群個數：23

[ 216, 28 ]:1,55,8,24,8,0,48,18,0,36,0,0,0,

0,共轭類數：36中心：[ 2, 1 ]換位子群：[ 27, 2 ]自同構群：1296正規子群個數：21

[ 216, 29 ]:1,73,8,6,44,0,12,18,0,36,0,0,0,

0,共轭類數：33中心：[ 2, 1 ]換位子群：[ 54, 9 ]自同構群：1296正規子群個數：19

[ 216, 30 ]:1,7,8,72,20,0,36,54,0,0,0,0,0,

0,共轭類數：36中心：[ 2, 1 ]換位子群：[ 27, 2 ]自同構群：1296正規子群個數：25

[ 216, 31 ]:1,25,8,54,56,0,0,54,0,0,0,0,0,

0,共轭類數：33中心：[ 2, 1 ]換位子群：[ 54, 9 ]自同構群：1296正規子群個數：19

[ 216, 32 ]:1,61,8,18,20,0,36,54,0,0,0,0,0,

0,共轭類數：33中心：[ 2, 1 ]換位子群：[ 54, 9 ]自同構群：1296正規子群個數：19

[ 216, 33 ]:1,1,26,54,26,0,108,0,0,0,0,0,0,

0,共轭類數：19中心：[ 2, 1 ]換位子群：[ 54, 10 ]自同構群：864正規子群個數：16

[ 216, 34 ]:1,19,26,36,62,0,72,0,0,0,0,0,0,

0,共轭類數：22中心：[ 2, 1 ]換位子群：[ 27, 3 ]自同構群：432正規子群個數：20

[ 216, 35 ]:1,37,26,18,98,0,36,0,0,0,0,0,0,

0,共轭類數：19中心：[ 2, 1 ]換位子群：[ 54, 10 ]自同構群：864正規子群個數：16

[ 216, 36 ]:1,19,26,36,62,0,72,0,0,0,0,0,0,

0,共轭類數：22中心：[ 2, 1 ]換位子群：[ 27, 3 ]自同構群：864正規子群個數：18

[ 216, 37 ]:1,37,26,18,98,0,36,0,0,0,0,0,0,

0,共轭類數：19中心：[ 2, 1 ]換位子群：[ 54, 10 ]自同構群：432正規子群個數：16

[ 216, 38 ]:1,1,26,6,26,0,12,54,0,36,0,0,0,

0,共轭類數：63中心：[ 18, 2 ]換位子群：[ 8, 4 ]自同構群：432正規子群個數：16

[ 216, 39 ]:1,1,26,6,26,0,12,54,0,36,0,0,0,

0,共轭類數：31中心：[ 6, 2 ]換位子群：[ 24, 11 ]自同構群：216正規子群個數：13

[ 216, 40 ]:1,1,8,6,8,0,48,72,0,0,0,0,0,

0,共轭類數：63中心：[ 18, 5 ]換位子群：[ 8, 4 ]自同構群：1296正規子群個數：22

[ 216, 41 ]:1,1,8,6,8,0,48,72,0,0,0,0,0,

0,共轭類數：31中心：[ 6, 2 ]換位子群：[ 24, 11 ]自同構群：648正規子群個數：13

[ 216, 42 ]:1,1,80,6,80,0,48,0,0,0,0,0,0,

0,共轭類數：31中心：[ 6, 2 ]換位子群：[ 24, 11 ]自同構群：1296正規子群個數：13

[ 216, 43 ]:1,1,8,38,8,0,88,18,0,36,0,0,0,

0,共轭類數：63中心：[ 6, 2 ]換位子群：[ 18, 2 ]自同構群：864正規子群個數：24

[ 216, 44 ]:1,1,8,14,8,0,40,18,0,108,0,0,0,

0,共轭類數：81中心：[ 18, 2 ]換位子群：[ 6, 2 ]自同構群：288正規子群個數：27

[ 216, 45 ]:1,19,8,20,44,0,52,18,0,36,0,0,0,

0,共轭類數：72中心：[ 12, 2 ]換位子群：[ 9, 1 ]自同構群：432正規子群個數：28

[ 216, 46 ]:1,37,8,2,80,0,16,18,0,36,0,0,0,

0,共轭類數：63中心：[ 6, 2 ]換位子群：[ 18, 2 ]自同構群：864正規子群個數：24

[ 216, 47 ]:1,7,8,8,20,0,28,54,0,72,0,0,0,

0,共轭類數：108中心：[ 36, 2 ]換位子群：[ 3, 1 ]自同構群：144正規子群個數：33

[ 216, 48 ]:1,13,8,2,32,0,16,90,0,36,0,0,0,

0,共轭類數：81中心：[ 18, 2 ]換位子群：[ 6, 2 ]自同構群：288正規子群個數：27

[ 216, 49 ]:1,1,26,38,26,0,124,0,0,0,0,0,0,

0,共轭類數：31中心：[ 2, 1 ]換位子群：[ 18, 5 ]自同構群：864正規子群個數：21

[ 216, 50 ]:1,19,26,20,62,0,88,0,0,0,0,0,0,

0,共轭類數：40中心：[ 4, 1 ]換位子群：[ 9, 2 ]自同構群：432正規子群個數：25

[ 216, 51 ]:1,37,26,2,98,0,52,0,0,0,0,0,0,

0,共轭類數：31中心：[ 2, 1 ]換位子群：[ 18, 5 ]自同構群：864正規子群個數：21

[ 216, 52 ]:1,1,8,38,8,0,88,18,0,36,0,0,0,

0,共轭類數：31中心：[ 2, 1 ]換位子群：[ 18, 2 ]自同構群：432正規子群個數：21

[ 216, 53 ]:1,19,8,20,44,0,52,18,0,36,0,0,0,

0,共轭類數：40中心：[ 4, 1 ]換位子群：[ 9, 1 ]自同構群：216正規子群個數：25

[ 216, 54 ]:1,37,8,2,80,0,16,18,0,36,0,0,0,

0,共轭類數：31中心：[ 2, 1 ]換位子群：[ 18, 2 ]自同構群：432正規子群個數：21

[ 216, 55 ]:1,3,8,36,24,0,72,54,0,0,0,0,0,

0,共轭類數：72中心：[ 12, 5 ]換位子群：[ 9, 1 ]自同構群：864正規子群個數：36

[ 216, 56 ]:1,3,8,12,24,0,24,54,0,72,0,0,0,

0,共轭類數：108中心：[ 36, 5 ]換位子群：[ 3, 1 ]自同構群：288正規子群個數：39

[ 216, 57 ]:1,21,8,18,60,0,36,54,0,0,0,0,0,

0,共轭類數：63中心：[ 6, 2 ]換位子群：[ 18, 2 ]自同構群：432正規子群個數：24

[ 216, 58 ]:1,9,8,6,36,0,12,90,0,36,0,0,0,

0,共轭類數：81中心：[ 18, 2 ]換位子群：[ 6, 2 ]自同構群：144正規子群個數：27

[ 216, 59 ]:1,3,26,36,78,0,72,0,0,0,0,0,0,

0,共轭類數：40中心：[ 4, 2 ]換位子群：[ 9, 2 ]自同構群：864正規子群個數：31

[ 216, 60 ]:1,21,26,18,114,0,36,0,0,0,0,0,0,

0,共轭類數：31中心：[ 2, 1 ]換位子群：[ 18, 5 ]自同構群：432正規子群個數：21

[ 216, 61 ]:1,3,8,36,24,0,72,54,0,0,0,0,0,

0,共轭類數：40中心：[ 4, 2 ]換位子群：[ 9, 1 ]自同構群：432正規子群個數：31

[ 216, 62 ]:1,21,8,18,60,0,36,54,0,0,0,0,0,

0,共轭類數：31中心：[ 2, 1 ]換位子群：[ 18, 2 ]自同構群：216正規子群個數：21

[ 216, 63 ]:1,1,8,110,8,0,16,18,0,36,0,0,0,

0,共轭類數：57中心：[ 2, 1 ]換位子群：[ 54, 9 ]自同構群：23328正規子群個數：33

[ 216, 64 ]:1,55,8,56,8,0,16,18,0,36,0,0,0,

0,共轭類數：60中心：[ 4, 1 ]換位子群：[ 27, 2 ]自同構群：11664正規子群個數：35

[ 216, 65 ]:1,109,8,2,8,0,16,18,0,36,0,0,0,

0,共轭類數：57中心：[ 2, 1 ]換位子群：[ 54, 9 ]自同構群：23328正規子群個數：33

[ 216, 66 ]:1,1,26,38,26,0,124,0,0,0,0,0,0,

0,共轭類數：31中心：[ 6, 2 ]換位子群：[ 54, 10 ]自同構群：3456正規子群個數：24

[ 216, 67 ]:1,19,26,20,62,0,88,0,0,0,0,0,0,

0,共轭類數：40中心：[ 12, 2 ]換位子群：[ 27, 3 ]自同構群：1728正規子群個數：26

[ 216, 68 ]:1,37,26,2,98,0,52,0,0,0,0,0,0,

0,共轭類數：31中心：[ 6, 2 ]換位子群：[ 54, 10 ]自同構群：3456正規子群個數：24

[ 216, 69 ]:1,3,8,108,24,0,0,54,0,0,0,0,0,

0,共轭類數：60中心：[ 4, 2 ]換位子群：[ 27, 2 ]自同構群：23328正規子群個數：53

[ 216, 70 ]:1,57,8,54,24,0,0,54,0,0,0,0,0,

0,共轭類數：57中心：[ 2, 1 ]換位子群：[ 54, 9 ]自同構群：11664正規子群個數：33

[ 216, 71 ]:1,3,26,36,78,0,72,0,0,0,0,0,0,

0,共轭類數：40中心：[ 12, 5 ]換位子群：[ 27, 3 ]自同構群：3456正規子群個數：38

[ 216, 72 ]:1,21,26,18,114,0,36,0,0,0,0,0,0,

0,共轭類數：31中心：[ 6, 2 ]換位子群：[ 54, 10 ]自同構群：1728正規子群個數：24

[ 216, 73 ]:1,3,8,4,24,0,32,54,0,72,0,0,0,

0,共轭類數：216中心：[ 216, 73 ]換位子群：[ 1, 1 ]自同構群：864正規子群個數：80

[ 216, 74 ]:1,3,26,4,78,0,104,0,0,0,0,0,0,

0,共轭類數：88中心：[ 24, 9 ]換位子群：[ 3, 1 ]自同構群：3456正規子群個數：56

[ 216, 75 ]:1,3,8,4,24,0,32,54,0,72,0,0,0,

0,共轭類數：88中心：[ 24, 9 ]換位子群：[ 3, 1 ]自同構群：432正規子群個數：56

[ 216, 76 ]:1,5,8,2,40,0,16,90,0,36,0,0,0,

0,共轭類數：135中心：[ 54, 9 ]換位子群：[ 2, 1 ]自同構群：864正規子群個數：60

[ 216, 77 ]:1,5,26,2,130,0,52,0,0,0,0,0,0,

0,共轭類數：55中心：[ 6, 2 ]換位子群：[ 6, 2 ]自同構群：3456正規子群個數：42

[ 216, 78 ]:1,5,8,2,40,0,16,90,0,36,0,0,0,

0,共轭類數：55中心：[ 6, 2 ]換位子群：[ 6, 2 ]自同構群：432正規子群個數：42

[ 216, 79 ]:1,1,8,6,8,0,48,18,0,108,0,0,0,

0,共轭類數：135中心：[ 54, 9 ]換位子群：[ 2, 1 ]自同構群：2592正規子群個數：60

[ 216, 80 ]:1,1,26,6,26,0,156,0,0,0,0,0,0,

0,共轭類數：55中心：[ 6, 2 ]換位子群：[ 6, 2 ]自同構群：10368正規子群個數：42

[ 216, 81 ]:1,1,8,6,8,0,48,18,0,108,0,0,0,

0,共轭類數：55中心：[ 6, 2 ]換位子群：[ 6, 2 ]自同構群：1296正規子群個數：42

[ 216, 82 ]:1,1,26,2,26,12,52,0,0,0,0,0,0,

0,共轭類數：108中心：[ 36, 8 ]換位子群：[ 3, 1 ]自同構群：1152正規子群個數：42

[ 216, 83 ]:1,1,26,2,26,36,52,0,0,0,0,0,0,

0,共轭類數：72中心：[ 12, 2 ]換位子群：[ 9, 2 ]自同構群：3456正規子群個數：38

[ 216, 84 ]:1,1,26,2,26,108,52,0,0,0,0,0,0,

0,共轭類數：60中心：[ 4, 1 ]換位子群：[ 27, 5 ]自同構群：1213056正規子群個數：85

[ 216, 85 ]:1,1,26,2,26,4,52,0,0,0,0,0,0,

0,共轭類數：216中心：[ 216, 85 ]換位子群：[ 1, 1 ]自同構群：44928正規子群個數：112

[ 216, 86 ]:1,9,26,18,18,108,36,0,0,0,0,0,0,

0,共轭類數：13中心：[ 1, 1 ]換位子群：[ 27, 3 ]自同構群：432正規子群個數：6

[ 216, 87 ]:1,45,26,18,90,0,36,0,0,0,0,0,0,

0,共轭類數：13中心：[ 1, 1 ]換位子群：[ 54, 8 ]自同構群：432正規子群個數：8

[ 216, 88 ]:1,9,26,54,18,0,108,0,0,0,0,0,0,

0,共轭類數：16中心：[ 3, 1 ]換位子群：[ 54, 8 ]自同構群：432正規子群個數：8

[ 216, 89 ]:1,9,26,6,18,0,12,54,0,36,0,0,0,

0,共轭類數：45中心：[ 9, 1 ]換位子群：[ 12, 3 ]自同構群：144正規子群個數：12

[ 216, 90 ]:1,21,8,18,60,0,36,0,0,0,0,0,0,

0,共轭類數：19中心：[ 1, 1 ]換位子群：[ 36, 3 ]自同構群：216正規子群個數：10

[ 216, 91 ]:1,21,8,18,60,0,36,0,0,0,0,0,0,

0,共轭類數：27中心：[ 3, 1 ]換位子群：[ 36, 3 ]自同構群：432正規子群個數：12

[ 216, 92 ]:1,21,80,18,60,0,36,0,0,0,0,0,0,

0,共轭類數：19中心：[ 1, 1 ]換位子群：[ 36, 11 ]自同構群：432正規子群個數：10

[ 216, 93 ]:1,57,26,54,6,0,0,18,0,0,0,0,0,

0,共轭類數：21中心：[ 1, 1 ]換位子群：[ 108, 18 ]自同構群：3888正規子群個數：14

[ 216, 94 ]:1,57,8,54,24,0,0,0,0,0,0,0,0,

0,共轭類數：21中心：[ 1, 1 ]換位子群：[ 108, 20 ]自同構群：11664正規子群個數：17

[ 216, 95 ]:1,21,80,18,60,0,36,0,0,0,0,0,0,

0,共轭類數：19中心：[ 3, 1 ]換位子群：[ 108, 22 ]自同構群：432正規子群個數：11

[ 216, 96 ]:1,39,26,0,78,0,0,18,0,0,0,0,0,

0,共轭類數：16中心：[ 1, 1 ]換位子群：[ 36, 5 ]自同構群：648正規子群個數：11

[ 216, 97 ]:1,39,26,0,78,0,0,18,0,0,0,0,0,

0,共轭類數：24中心：[ 1, 1 ]換位子群：[ 36, 5 ]自同構群：1296正規子群個數：12

[ 216, 98 ]:1,15,8,0,48,0,0,72,0,0,0,0,0,

0,共轭類數：36中心：[ 3, 1 ]換位子群：[ 12, 5 ]自同構群：432正規子群個數：15

[ 216, 99 ]:1,39,80,0,96,0,0,0,0,0,0,0,0,

0,共轭類數：16中心：[ 1, 1 ]換位子群：[ 36, 14 ]自同構群：1296正規子群個數：11

[ 216, 100 ]:1,19,26,36,62,0,72,0,0,0,0,0,0,

0,共轭類數：28中心：[ 6, 2 ]換位子群：[ 27, 3 ]自同構群：288正規子群個數：12

[ 216, 101 ]:1,79,8,0,56,0,0,54,0,0,0,0,0,

0,共轭類數：36中心：[ 2, 1 ]換位子群：[ 27, 2 ]自同構群：1296正規子群個數：35

[ 216, 102 ]:1,55,26,0,134,0,0,0,0,0,0,0,0,

0,共轭類數：22中心：[ 2, 1 ]換位子群：[ 27, 3 ]自同構群：864正規子群個數：30

[ 216, 103 ]:1,7,26,0,38,0,0,90,0,0,0,0,0,

0,共轭類數：72中心：[ 18, 2 ]換位子群：[ 4, 2 ]自同構群：432正規子群個數：26

[ 216, 104 ]:1,7,26,0,38,0,0,90,0,0,0,0,0,

0,共轭類數：40中心：[ 6, 2 ]換位子群：[ 12, 5 ]自同構群：216正規子群個數：20

[ 216, 105 ]:1,7,8,0,56,0,0,72,0,0,0,0,0,

0,共轭類數：72中心：[ 18, 5 ]換位子群：[ 4, 2 ]自同構群：1296正規子群個數：32

[ 216, 106 ]:1,7,8,0,56,0,0,72,0,0,0,0,0,

0,共轭類數：40中心：[ 6, 2 ]換位子群：[ 12, 5 ]自同構群：648正規子群個數：20

[ 216, 107 ]:1,7,80,0,128,0,0,0,0,0,0,0,0,

0,共轭類數：40中心：[ 6, 2 ]換位子群：[ 12, 5 ]自同構群：1296正規子群個數：20

[ 216, 108 ]:1,39,8,0,96,0,0,54,0,0,0,0,0,

0,共轭類數：72中心：[ 12, 5 ]換位子群：[ 9, 1 ]自同構群：2592正規子群個數：52

[ 216, 109 ]:1,15,8,0,48,0,0,126,0,0,0,0,0,

0,共轭類數：108中心：[ 36, 5 ]換位子群：[ 3, 1 ]自同構群：864正規子群個數：63

[ 216, 110 ]:1,39,26,0,150,0,0,0,0,0,0,0,0,

0,共轭類數：40中心：[ 4, 2 ]換位子群：[ 9, 2 ]自同構群：2592正規子群個數：47

[ 216, 111 ]:1,39,8,0,96,0,0,54,0,0,0,0,0,

0,共轭類數：40中心：[ 4, 2 ]換位子群：[ 9, 1 ]自同構群：1296正規子群個數：47

[ 216, 112 ]:1,111,8,0,24,0,0,54,0,0,0,0,0,

0,共轭類數：60中心：[ 4, 2 ]換位子群：[ 27, 2 ]自同構群：69984正規子群個數：61

[ 216, 113 ]:1,39,26,0,150,0,0,0,0,0,0,0,0,

0,共轭類數：40中心：[ 12, 5 ]換位子群：[ 27, 3 ]自同構群：10368正規子群個數：46

[ 216, 114 ]:1,7,8,0,56,0,0,126,0,0,0,0,0,

0,共轭類數：216中心：[ 216, 114 ]換位子群：[ 1, 1 ]自同構群：18144正規子群個數：160

[ 216, 115 ]:1,7,26,0,182,0,0,0,0,0,0,0,0,

0,共轭類數：88中心：[ 24, 15 ]換位子群：[ 3, 1 ]自同構群：72576正規子群個數：112

[ 216, 116 ]:1,7,8,0,56,0,0,126,0,0,0,0,0,

0,共轭類數：88中心：[ 24, 15 ]換位子群：[ 3, 1 ]自同構群：9072正規子群個數：112

[ 216, 117 ]:1,1,26,18,26,36,36,0,0,0,0,0,0,

0,共轭類數：36中心：[ 6, 2 ]換位子群：[ 9, 2 ]自同構群：576正規子群個數：12

[ 216, 118 ]:1,1,26,18,26,108,36,0,0,0,0,0,0,

0,共轭類數：24中心：[ 2, 1 ]換位子群：[ 27, 5 ]自同構群：1728正規子群個數：11

[ 216, 119 ]:1,7,26,24,74,0,84,0,0,0,0,0,0,

0,共轭類數：54中心：[ 6, 2 ]換位子群：[ 9, 2 ]自同構群：288正規子群個數：36

[ 216, 120 ]:1,19,26,12,62,0,96,0,0,0,0,0,0,

0,共轭類數：54中心：[ 6, 2 ]換位子群：[ 9, 2 ]自同構群：576正規子群個數：32

[ 216, 121 ]:1,13,26,18,122,0,36,0,0,0,0,0,0,

0,共轭類數：45中心：[ 6, 2 ]換位子群：[ 18, 5 ]自同構群：576正規子群個數：28

[ 216, 122 ]:1,25,26,6,110,0,48,0,0,0,0,0,0,

0,共轭類數：45中心：[ 6, 2 ]換位子群：[ 18, 5 ]自同構群：288正規子群個數：28

[ 216, 123 ]:1,1,26,30,26,0,132,0,0,0,0,0,0,

0,共轭類數：45中心：[ 6, 2 ]換位子群：[ 18, 5 ]自同構群：576正規子群個數：28

[ 216, 124 ]:1,7,26,72,74,0,36,0,0,0,0,0,0,

0,共轭類數：36中心：[ 2, 1 ]換位子群：[ 27, 5 ]自同構群：10368正規子群個數：46

[ 216, 125 ]:1,19,26,60,62,0,48,0,0,0,0,0,0,

0,共轭類數：36中心：[ 2, 1 ]換位子群：[ 27, 5 ]自同構群：10368正規子群個數：38

[ 216, 126 ]:1,55,26,24,26,0,84,0,0,0,0,0,0,

0,共轭類數：36中心：[ 2, 1 ]換位子群：[ 27, 5 ]自同構群：10368正規子群個數：36

[ 216, 127 ]:1,25,26,54,110,0,0,0,0,0,0,0,0,

0,共轭類數：33中心：[ 2, 1 ]換位子群：[ 54, 15 ]自同構群：10368正規子群個數：34

[ 216, 128 ]:1,61,26,18,74,0,36,0,0,0,0,0,0,

0,共轭類數：33中心：[ 2, 1 ]換位子群：[ 54, 15 ]自同構群：10368正規子群個數：34

[ 216, 129 ]:1,73,26,6,62,0,48,0,0,0,0,0,0,

0,共轭類數：33中心：[ 2, 1 ]換位子群：[ 54, 15 ]自同構群：10368正規子群個數：34

[ 216, 130 ]:1,1,26,78,26,0,84,0,0,0,0,0,0,

0,共轭類數：33中心：[ 2, 1 ]換位子群：[ 54, 15 ]自同構群：10368正規子群個數：34

[ 216, 131 ]:1,19,26,36,62,0,72,0,0,0,0,0,0,

0,共轭類數：30中心：[ 2, 1 ]換位子群：[ 27, 5 ]自同構群：1728正規子群個數：27

[ 216, 132 ]:1,37,26,18,98,0,36,0,0,0,0,0,0,

0,共轭類數：27中心：[ 2, 1 ]換位子群：[ 54, 15 ]自同構群：1728正規子群個數：23

[ 216, 133 ]:1,1,26,54,26,0,108,0,0,0,0,0,0,

0,共轭類數：27中心：[ 2, 1 ]換位子群：[ 54, 15 ]自同構群：5184正規子群個數：23

[ 216, 134 ]:1,1,80,6,80,0,48,0,0,0,0,0,0,

0,共轭類數：63中心：[ 18, 5 ]換位子群：[ 8, 4 ]自同構群：10368正規子群個數：40

[ 216, 135 ]:1,1,26,14,26,0,148,0,0,0,0,0,0,

0,共轭類數：81中心：[ 18, 5 ]換位子群：[ 6, 2 ]自同構群：2304正規子群個數：54

[ 216, 136 ]:1,7,26,8,74,0,100,0,0,0,0,0,0,

0,共轭類數：108中心：[ 36, 8 ]換位子群：[ 3, 1 ]自同構群：1152正規子群個數：66

[ 216, 137 ]:1,13,26,2,122,0,52,0,0,0,0,0,0,

0,共轭類數：81中心：[ 18, 5 ]換位子群：[ 6, 2 ]自同構群：2304正規子群個數：54

[ 216, 138 ]:1,3,26,12,78,0,96,0,0,0,0,0,0,

0,共轭類數：108中心：[ 36, 14 ]換位子群：[ 3, 1 ]自同構群：2304正規子群個數：78

[ 216, 139 ]:1,9,26,6,126,0,48,0,0,0,0,0,0,

0,共轭類數：81中心：[ 18, 5 ]換位子群：[ 6, 2 ]自同構群：1152正規子群個數：54

[ 216, 140 ]:1,1,26,38,26,0,124,0,0,0,0,0,0,

0,共轭類數：63中心：[ 6, 2 ]換位子群：[ 18, 5 ]自同構群：6912正規子群個數：42

[ 216, 141 ]:1,19,26,20,62,0,88,0,0,0,0,0,0,

0,共轭類數：72中心：[ 12, 2 ]換位子群：[ 9, 2 ]自同構群：3456正規子群個數：46

[ 216, 142 ]:1,37,26,2,98,0,52,0,0,0,0,0,0,

0,共轭類數：63中心：[ 6, 2 ]換位子群：[ 18, 5 ]自同構群：6912正規子群個數：42

[ 216, 143 ]:1,3,26,36,78,0,72,0,0,0,0,0,0,

0,共轭類數：72中心：[ 12, 5 ]換位子群：[ 9, 2 ]自同構群：6912正規子群個數：66

[ 216, 144 ]:1,21,26,18,114,0,36,0,0,0,0,0,0,

0,共轭類數：63中心：[ 6, 2 ]換位子群：[ 18, 5 ]自同構群：3456正規子群個數：42

[ 216, 145 ]:1,1,26,110,26,0,52,0,0,0,0,0,0,

0,共轭類數：57中心：[ 2, 1 ]換位子群：[ 54, 15 ]自同構群：2426112正規子群個數：87

[ 216, 146 ]:1,55,26,56,26,0,52,0,0,0,0,0,0,

0,共轭類數：60中心：[ 4, 1 ]換位子群：[ 27, 5 ]自同構群：1213056正規子群個數：89

[ 216, 147 ]:1,109,26,2,26,0,52,0,0,0,0,0,0,

0,共轭類數：57中心：[ 2, 1 ]換位子群：[ 54, 15 ]自同構群：2426112正規子群個數：87

[ 216, 148 ]:1,3,26,108,78,0,0,0,0,0,0,0,0,

0,共轭類數：60中心：[ 4, 2 ]換位子群：[ 27, 5 ]自同構群：2426112正規子群個數：143

[ 216, 149 ]:1,57,26,54,78,0,0,0,0,0,0,0,0,

0,共轭類數：57中心：[ 2, 1 ]換位子群：[ 54, 15 ]自同構群：1213056正規子群個數：87

[ 216, 150 ]:1,3,26,4,78,0,104,0,0,0,0,0,0,

0,共轭類數：216中心：[ 216, 150 ]換位子群：[ 1, 1 ]自同構群：89856正規子群個數：224

[ 216, 151 ]:1,5,26,2,130,0,52,0,0,0,0,0,0,

0,共轭類數：135中心：[ 54, 15 ]換位子群：[ 2, 1 ]自同構群：89856正規子群個數：168

[ 216, 152 ]:1,1,26,6,26,0,156,0,0,0,0,0,0,

0,共轭類數：135中心：[ 54, 15 ]換位子群：[ 2, 1 ]自同構群：269568正規子群個數：168

[ 216, 153 ]:1,9,80,54,72,0,0,0,0,0,0,0,0,

0,共轭類數：10中心：[ 1, 1 ]換位子群：[ 72, 41 ]自同構群：432正規子群個數：5

[ 216, 154 ]:1,9,26,18,18,36,36,0,0,0,0,0,0,

0,共轭類數：27中心：[ 3, 1 ]換位子群：[ 9, 2 ]自同構群：288正規子群個數：10

[ 216, 155 ]:1,9,26,18,18,108,36,0,0,0,0,0,0,

0,共轭類數：15中心：[ 1, 1 ]換位子群：[ 27, 5 ]自同構群：864正規子群個數：9

[ 216, 156 ]:1,39,26,72,42,0,36,0,0,0,0,0,0,

0,共轭類數：18中心：[ 1, 1 ]換位子群：[ 27, 5 ]自同構群：864正規子群個數：14

[ 216, 157 ]:1,21,26,18,114,0,36,0,0,0,0,0,0,

0,共轭類數：27中心：[ 3, 1 ]換位子群：[ 18, 4 ]自同構群：288正規子群個數：14

[ 216, 158 ]:1,33,26,54,102,0,0,0,0,0,0,0,0,

0,共轭類數：18中心：[ 1, 1 ]換位子群：[ 54, 13 ]自同構群：432正規子群個數：11

[ 216, 159 ]:1,45,26,18,90,0,36,0,0,0,0,0,0,

0,共轭類數：15中心：[ 1, 1 ]換位子群：[ 54, 13 ]自同構群：864正規子群個數：11

[ 216, 160 ]:1,9,26,54,18,0,108,0,0,0,0,0,0,

0,共轭類數：18中心：[ 3, 1 ]換位子群：[ 18, 4 ]自同構群：864正規子群個數：14

[ 216, 161 ]:1,9,26,126,18,0,36,0,0,0,0,0,0,

0,共轭類數：12中心：[ 1, 1 ]換位子群：[ 54, 13 ]自同構群：864正規子群個數：11

[ 216, 162 ]:1,63,26,0,126,0,0,0,0,0,0,0,0,

0,共轭類數：27中心：[ 1, 1 ]換位子群：[ 27, 5 ]自同構群：1296正規子群個數：38

[ 216, 163 ]:1,9,80,6,72,0,48,0,0,0,0,0,0,

0,共轭類數：45中心：[ 9, 2 ]換位子群：[ 12, 3 ]自同構群：1152正規子群個數：24

[ 216, 164 ]:1,21,80,18,60,0,36,0,0,0,0,0,0,

0,共轭類數：27中心：[ 3, 1 ]換位子群：[ 36, 11 ]自同構群：864正規子群個數：18

[ 216, 165 ]:1,57,80,54,24,0,0,0,0,0,0,0,0,

0,共轭類數：21中心：[ 1, 1 ]換位子群：[ 108, 41 ]自同構群：93312正規子群個數：35

[ 216, 166 ]:1,15,80,0,120,0,0,0,0,0,0,0,0,

0,共轭類數：36中心：[ 3, 1 ]換位子群：[ 12, 5 ]自同構群：864正規子群個數：24

[ 216, 167 ]:1,39,80,0,96,0,0,0,0,0,0,0,0,

0,共轭類數：24中心：[ 1, 1 ]換位子群：[ 36, 14 ]自同構群：10368正規子群個數：21

[ 216, 168 ]:1,19,26,36,62,0,72,0,0,0,0,0,0,

0,共轭類數：36中心：[ 6, 2 ]換位子群：[ 9, 2 ]自同構群：576正規子群個數：20

[ 216, 169 ]:1,19,26,108,62,0,0,0,0,0,0,0,0,

0,共轭類數：24中心：[ 2, 1 ]換位子群：[ 27, 5 ]自同構群：1728正規子群個數：17

[ 216, 170 ]:1,31,26,0,158,0,0,0,0,0,0,0,0,

0,共轭類數：54中心：[ 6, 2 ]換位子群：[ 9, 2 ]自同構群：576正規子群個數：56

[ 216, 171 ]:1,79,26,0,110,0,0,0,0,0,0,0,0,

0,共轭類數：36中心：[ 2, 1 ]換位子群：[ 27, 5 ]自同構群：10368正規子群個數：56

[ 216, 172 ]:1,55,26,0,134,0,0,0,0,0,0,0,0,

0,共轭類數：30中心：[ 2, 1 ]換位子群：[ 27, 5 ]自同構群：5184正規子群個數：39

[ 216, 173 ]:1,7,80,0,128,0,0,0,0,0,0,0,0,

0,共轭類數：72中心：[ 18, 5 ]換位子群：[ 4, 2 ]自同構群：10368正規子群個數：68

[ 216, 174 ]:1,15,26,0,174,0,0,0,0,0,0,0,0,

0,共轭類數：108中心：[ 36, 14 ]換位子群：[ 3, 1 ]自同構群：6912正規子群個數：126

[ 216, 175 ]:1,39,26,0,150,0,0,0,0,0,0,0,0,

0,共轭類數：72中心：[ 12, 5 ]換位子群：[ 9, 2 ]自同構群：20736正規子群個數：82

[ 216, 176 ]:1,111,26,0,78,0,0,0,0,0,0,0,0,

0,共轭類數：60中心：[ 4, 2 ]換位子群：[ 27, 5 ]自同構群：7278336正規子群個數：151

[ 216, 177 ]:1,7,26,0,182,0,0,0,0,0,0,0,0,

0,共轭類數：216中心：[ 216, 177 ]換位子群：[ 1, 1 ]自同構群：1886976正規子群個數：448