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G = C92.C4order 368 = 24·23

1st non-split extension by C92 of C4 acting via C4/C2=C2

metacyclic, supersoluble, monomial, 2-hyperelementary

Aliases: C92.1C4, C4.Dic23, C4.15D46, C232M4(2), C22.Dic23, C92.15C22, C23⋊C85C2, (C2×C46).3C4, (C2×C92).5C2, C46.7(C2×C4), (C2×C4).2D23, C2.3(C2×Dic23), SmallGroup(368,9)

Series: Derived Chief Lower central Upper central

C1C46 — C92.C4
C1C23C46C92C23⋊C8 — C92.C4
C23C46 — C92.C4
C1C4C2×C4

Generators and relations for C92.C4
 G = < a,b | a92=1, b4=a46, bab-1=a-1 >

2C2
2C46
23C8
23C8
23M4(2)

Smallest permutation representation of C92.C4
On 184 points
Generators in S184
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92)(93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184)
(1 175 70 106 47 129 24 152)(2 174 71 105 48 128 25 151)(3 173 72 104 49 127 26 150)(4 172 73 103 50 126 27 149)(5 171 74 102 51 125 28 148)(6 170 75 101 52 124 29 147)(7 169 76 100 53 123 30 146)(8 168 77 99 54 122 31 145)(9 167 78 98 55 121 32 144)(10 166 79 97 56 120 33 143)(11 165 80 96 57 119 34 142)(12 164 81 95 58 118 35 141)(13 163 82 94 59 117 36 140)(14 162 83 93 60 116 37 139)(15 161 84 184 61 115 38 138)(16 160 85 183 62 114 39 137)(17 159 86 182 63 113 40 136)(18 158 87 181 64 112 41 135)(19 157 88 180 65 111 42 134)(20 156 89 179 66 110 43 133)(21 155 90 178 67 109 44 132)(22 154 91 177 68 108 45 131)(23 153 92 176 69 107 46 130)

G:=sub<Sym(184)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92)(93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184), (1,175,70,106,47,129,24,152)(2,174,71,105,48,128,25,151)(3,173,72,104,49,127,26,150)(4,172,73,103,50,126,27,149)(5,171,74,102,51,125,28,148)(6,170,75,101,52,124,29,147)(7,169,76,100,53,123,30,146)(8,168,77,99,54,122,31,145)(9,167,78,98,55,121,32,144)(10,166,79,97,56,120,33,143)(11,165,80,96,57,119,34,142)(12,164,81,95,58,118,35,141)(13,163,82,94,59,117,36,140)(14,162,83,93,60,116,37,139)(15,161,84,184,61,115,38,138)(16,160,85,183,62,114,39,137)(17,159,86,182,63,113,40,136)(18,158,87,181,64,112,41,135)(19,157,88,180,65,111,42,134)(20,156,89,179,66,110,43,133)(21,155,90,178,67,109,44,132)(22,154,91,177,68,108,45,131)(23,153,92,176,69,107,46,130)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92)(93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184), (1,175,70,106,47,129,24,152)(2,174,71,105,48,128,25,151)(3,173,72,104,49,127,26,150)(4,172,73,103,50,126,27,149)(5,171,74,102,51,125,28,148)(6,170,75,101,52,124,29,147)(7,169,76,100,53,123,30,146)(8,168,77,99,54,122,31,145)(9,167,78,98,55,121,32,144)(10,166,79,97,56,120,33,143)(11,165,80,96,57,119,34,142)(12,164,81,95,58,118,35,141)(13,163,82,94,59,117,36,140)(14,162,83,93,60,116,37,139)(15,161,84,184,61,115,38,138)(16,160,85,183,62,114,39,137)(17,159,86,182,63,113,40,136)(18,158,87,181,64,112,41,135)(19,157,88,180,65,111,42,134)(20,156,89,179,66,110,43,133)(21,155,90,178,67,109,44,132)(22,154,91,177,68,108,45,131)(23,153,92,176,69,107,46,130) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92),(93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184)], [(1,175,70,106,47,129,24,152),(2,174,71,105,48,128,25,151),(3,173,72,104,49,127,26,150),(4,172,73,103,50,126,27,149),(5,171,74,102,51,125,28,148),(6,170,75,101,52,124,29,147),(7,169,76,100,53,123,30,146),(8,168,77,99,54,122,31,145),(9,167,78,98,55,121,32,144),(10,166,79,97,56,120,33,143),(11,165,80,96,57,119,34,142),(12,164,81,95,58,118,35,141),(13,163,82,94,59,117,36,140),(14,162,83,93,60,116,37,139),(15,161,84,184,61,115,38,138),(16,160,85,183,62,114,39,137),(17,159,86,182,63,113,40,136),(18,158,87,181,64,112,41,135),(19,157,88,180,65,111,42,134),(20,156,89,179,66,110,43,133),(21,155,90,178,67,109,44,132),(22,154,91,177,68,108,45,131),(23,153,92,176,69,107,46,130)])

98 conjugacy classes

class 1 2A2B4A4B4C8A8B8C8D23A···23K46A···46AG92A···92AR
order122444888823···2346···4692···92
size112112464646462···22···22···2

98 irreducible representations

dim11111222222
type++++-+-
imageC1C2C2C4C4M4(2)D23Dic23D46Dic23C92.C4
kernelC92.C4C23⋊C8C2×C92C92C2×C46C23C2×C4C4C4C22C1
# reps1212221111111144

Matrix representation of C92.C4 in GL2(𝔽1289) generated by

620
1052894
,
10941223
647195
G:=sub<GL(2,GF(1289))| [62,1052,0,894],[1094,647,1223,195] >;

C92.C4 in GAP, Magma, Sage, TeX

C_{92}.C_4
% in TeX

G:=Group("C92.C4");
// GroupNames label

G:=SmallGroup(368,9);
// by ID

G=gap.SmallGroup(368,9);
# by ID

G:=PCGroup([5,-2,-2,-2,-2,-23,20,101,42,8804]);
// Polycyclic

G:=Group<a,b|a^92=1,b^4=a^46,b*a*b^-1=a^-1>;
// generators/relations

Export

Subgroup lattice of C92.C4 in TeX

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