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G = D925C2order 368 = 24·23

The semidirect product of D92 and C2 acting through Inn(D92)

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D925C2, C4.16D46, Dic465C2, C46.4C23, C22.2D46, C92.16C22, D46.1C22, Dic23.2C22, (C2×C92)⋊4C2, (C2×C4)⋊3D23, (C4×D23)⋊4C2, C231(C4○D4), C23⋊D43C2, C2.5(C22×D23), (C2×C46).11C22, SmallGroup(368,30)

Series: Derived Chief Lower central Upper central

C1C46 — D925C2
C1C23C46D46C4×D23 — D925C2
C23C46 — D925C2
C1C4C2×C4

Generators and relations for D925C2
 G = < a,b,c | a92=b2=c2=1, bab=a-1, ac=ca, cbc=a46b >

2C2
46C2
46C2
23C4
23C4
23C22
23C22
2C46
2D23
2D23
23C2×C4
23D4
23D4
23D4
23C2×C4
23Q8
23C4○D4

Smallest permutation representation of D925C2
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 23)(2 22)(3 21)(4 20)(5 19)(6 18)(7 17)(8 16)(9 15)(10 14)(11 13)(24 92)(25 91)(26 90)(27 89)(28 88)(29 87)(30 86)(31 85)(32 84)(33 83)(34 82)(35 81)(36 80)(37 79)(38 78)(39 77)(40 76)(41 75)(42 74)(43 73)(44 72)(45 71)(46 70)(47 69)(48 68)(49 67)(50 66)(51 65)(52 64)(53 63)(54 62)(55 61)(56 60)(57 59)(93 177)(94 176)(95 175)(96 174)(97 173)(98 172)(99 171)(100 170)(101 169)(102 168)(103 167)(104 166)(105 165)(106 164)(107 163)(108 162)(109 161)(110 160)(111 159)(112 158)(113 157)(114 156)(115 155)(116 154)(117 153)(118 152)(119 151)(120 150)(121 149)(122 148)(123 147)(124 146)(125 145)(126 144)(127 143)(128 142)(129 141)(130 140)(131 139)(132 138)(133 137)(134 136)(178 184)(179 183)(180 182)
(1 101)(2 102)(3 103)(4 104)(5 105)(6 106)(7 107)(8 108)(9 109)(10 110)(11 111)(12 112)(13 113)(14 114)(15 115)(16 116)(17 117)(18 118)(19 119)(20 120)(21 121)(22 122)(23 123)(24 124)(25 125)(26 126)(27 127)(28 128)(29 129)(30 130)(31 131)(32 132)(33 133)(34 134)(35 135)(36 136)(37 137)(38 138)(39 139)(40 140)(41 141)(42 142)(43 143)(44 144)(45 145)(46 146)(47 147)(48 148)(49 149)(50 150)(51 151)(52 152)(53 153)(54 154)(55 155)(56 156)(57 157)(58 158)(59 159)(60 160)(61 161)(62 162)(63 163)(64 164)(65 165)(66 166)(67 167)(68 168)(69 169)(70 170)(71 171)(72 172)(73 173)(74 174)(75 175)(76 176)(77 177)(78 178)(79 179)(80 180)(81 181)(82 182)(83 183)(84 184)(85 93)(86 94)(87 95)(88 96)(89 97)(90 98)(91 99)(92 100)

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

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

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

98 conjugacy classes

class 1 2A2B2C2D4A4B4C4D4E23A···23K46A···46AG92A···92AR
order122224444423···2346···4692···92
size112464611246462···22···22···2

98 irreducible representations

dim11111122222
type+++++++++
imageC1C2C2C2C2C2C4○D4D23D46D46D925C2
kernelD925C2Dic46C4×D23D92C23⋊D4C2×C92C23C2×C4C4C22C1
# reps112121211221144

Matrix representation of D925C2 in GL2(𝔽277) generated by

1150
108135
,
200179
26477
,
27477
1333
G:=sub<GL(2,GF(277))| [1,108,150,135],[200,264,179,77],[274,133,77,3] >;

D925C2 in GAP, Magma, Sage, TeX

D_{92}\rtimes_5C_2
% in TeX

G:=Group("D92:5C2");
// GroupNames label

G:=SmallGroup(368,30);
// by ID

G=gap.SmallGroup(368,30);
# by ID

G:=PCGroup([5,-2,-2,-2,-2,-23,46,182,8804]);
// Polycyclic

G:=Group<a,b,c|a^92=b^2=c^2=1,b*a*b=a^-1,a*c=c*a,c*b*c=a^46*b>;
// generators/relations

Export

Subgroup lattice of D925C2 in TeX

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