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G = C22×C46order 184 = 23·23

Abelian group of type [2,2,46]

direct product, abelian, monomial, 2-elementary

Aliases: C22×C46, SmallGroup(184,12)

Series: Derived Chief Lower central Upper central

C1 — C22×C46
C1C23C46C2×C46 — C22×C46
C1 — C22×C46
C1 — C22×C46

Generators and relations for C22×C46
 G = < a,b,c | a2=b2=c46=1, ab=ba, ac=ca, bc=cb >


Smallest permutation representation of C22×C46
Regular action on 184 points
Generators in S184
(1 125)(2 126)(3 127)(4 128)(5 129)(6 130)(7 131)(8 132)(9 133)(10 134)(11 135)(12 136)(13 137)(14 138)(15 93)(16 94)(17 95)(18 96)(19 97)(20 98)(21 99)(22 100)(23 101)(24 102)(25 103)(26 104)(27 105)(28 106)(29 107)(30 108)(31 109)(32 110)(33 111)(34 112)(35 113)(36 114)(37 115)(38 116)(39 117)(40 118)(41 119)(42 120)(43 121)(44 122)(45 123)(46 124)(47 141)(48 142)(49 143)(50 144)(51 145)(52 146)(53 147)(54 148)(55 149)(56 150)(57 151)(58 152)(59 153)(60 154)(61 155)(62 156)(63 157)(64 158)(65 159)(66 160)(67 161)(68 162)(69 163)(70 164)(71 165)(72 166)(73 167)(74 168)(75 169)(76 170)(77 171)(78 172)(79 173)(80 174)(81 175)(82 176)(83 177)(84 178)(85 179)(86 180)(87 181)(88 182)(89 183)(90 184)(91 139)(92 140)
(1 73)(2 74)(3 75)(4 76)(5 77)(6 78)(7 79)(8 80)(9 81)(10 82)(11 83)(12 84)(13 85)(14 86)(15 87)(16 88)(17 89)(18 90)(19 91)(20 92)(21 47)(22 48)(23 49)(24 50)(25 51)(26 52)(27 53)(28 54)(29 55)(30 56)(31 57)(32 58)(33 59)(34 60)(35 61)(36 62)(37 63)(38 64)(39 65)(40 66)(41 67)(42 68)(43 69)(44 70)(45 71)(46 72)(93 181)(94 182)(95 183)(96 184)(97 139)(98 140)(99 141)(100 142)(101 143)(102 144)(103 145)(104 146)(105 147)(106 148)(107 149)(108 150)(109 151)(110 152)(111 153)(112 154)(113 155)(114 156)(115 157)(116 158)(117 159)(118 160)(119 161)(120 162)(121 163)(122 164)(123 165)(124 166)(125 167)(126 168)(127 169)(128 170)(129 171)(130 172)(131 173)(132 174)(133 175)(134 176)(135 177)(136 178)(137 179)(138 180)
(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)

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

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

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

C22×C46 is a maximal subgroup of   C23.D23

184 conjugacy classes

class 1 2A···2G23A···23V46A···46EX
order12···223···2346···46
size11···11···11···1

184 irreducible representations

dim1111
type++
imageC1C2C23C46
kernelC22×C46C2×C46C23C22
# reps1722154

Matrix representation of C22×C46 in GL3(𝔽47) generated by

100
0460
0046
,
4600
010
0046
,
2400
0380
0027
G:=sub<GL(3,GF(47))| [1,0,0,0,46,0,0,0,46],[46,0,0,0,1,0,0,0,46],[24,0,0,0,38,0,0,0,27] >;

C22×C46 in GAP, Magma, Sage, TeX

C_2^2\times C_{46}
% in TeX

G:=Group("C2^2xC46");
// GroupNames label

G:=SmallGroup(184,12);
// by ID

G=gap.SmallGroup(184,12);
# by ID

G:=PCGroup([4,-2,-2,-2,-23]);
// Polycyclic

G:=Group<a,b,c|a^2=b^2=c^46=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations

Export

Subgroup lattice of C22×C46 in TeX

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