direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C23×D23, C23⋊C24, C46⋊C23, (C22×C46)⋊3C2, (C2×C46)⋊4C22, SmallGroup(368,41)
Series: Derived ►Chief ►Lower central ►Upper central
| C23 — C23×D23 |
Generators and relations for C23×D23
G = < a,b,c,d,e | a2=b2=c2=d23=e2=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede=d-1 >
Subgroups: 1256 in 134 conjugacy classes, 83 normal (5 characteristic)
C1, C2, C2, C22, C22, C23, C23, C24, C23, D23, C46, D46, C2×C46, C22×D23, C22×C46, C23×D23
Quotients: C1, C2, C22, C23, C24, D23, D46, C22×D23, C23×D23
►On 184 points
Generators in S184
(1 104)(2 105)(3 106)(4 107)(5 108)(6 109)(7 110)(8 111)(9 112)(10 113)(11 114)(12 115)(13 93)(14 94)(15 95)(16 96)(17 97)(18 98)(19 99)(20 100)(21 101)(22 102)(23 103)(24 122)(25 123)(26 124)(27 125)(28 126)(29 127)(30 128)(31 129)(32 130)(33 131)(34 132)(35 133)(36 134)(37 135)(38 136)(39 137)(40 138)(41 116)(42 117)(43 118)(44 119)(45 120)(46 121)(47 148)(48 149)(49 150)(50 151)(51 152)(52 153)(53 154)(54 155)(55 156)(56 157)(57 158)(58 159)(59 160)(60 161)(61 139)(62 140)(63 141)(64 142)(65 143)(66 144)(67 145)(68 146)(69 147)(70 169)(71 170)(72 171)(73 172)(74 173)(75 174)(76 175)(77 176)(78 177)(79 178)(80 179)(81 180)(82 181)(83 182)(84 183)(85 184)(86 162)(87 163)(88 164)(89 165)(90 166)(91 167)(92 168)
(1 87)(2 88)(3 89)(4 90)(5 91)(6 92)(7 70)(8 71)(9 72)(10 73)(11 74)(12 75)(13 76)(14 77)(15 78)(16 79)(17 80)(18 81)(19 82)(20 83)(21 84)(22 85)(23 86)(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 47)(45 48)(46 49)(93 175)(94 176)(95 177)(96 178)(97 179)(98 180)(99 181)(100 182)(101 183)(102 184)(103 162)(104 163)(105 164)(106 165)(107 166)(108 167)(109 168)(110 169)(111 170)(112 171)(113 172)(114 173)(115 174)(116 145)(117 146)(118 147)(119 148)(120 149)(121 150)(122 151)(123 152)(124 153)(125 154)(126 155)(127 156)(128 157)(129 158)(130 159)(131 160)(132 161)(133 139)(134 140)(135 141)(136 142)(137 143)(138 144)
(1 38)(2 39)(3 40)(4 41)(5 42)(6 43)(7 44)(8 45)(9 46)(10 24)(11 25)(12 26)(13 27)(14 28)(15 29)(16 30)(17 31)(18 32)(19 33)(20 34)(21 35)(22 36)(23 37)(47 70)(48 71)(49 72)(50 73)(51 74)(52 75)(53 76)(54 77)(55 78)(56 79)(57 80)(58 81)(59 82)(60 83)(61 84)(62 85)(63 86)(64 87)(65 88)(66 89)(67 90)(68 91)(69 92)(93 125)(94 126)(95 127)(96 128)(97 129)(98 130)(99 131)(100 132)(101 133)(102 134)(103 135)(104 136)(105 137)(106 138)(107 116)(108 117)(109 118)(110 119)(111 120)(112 121)(113 122)(114 123)(115 124)(139 183)(140 184)(141 162)(142 163)(143 164)(144 165)(145 166)(146 167)(147 168)(148 169)(149 170)(150 171)(151 172)(152 173)(153 174)(154 175)(155 176)(156 177)(157 178)(158 179)(159 180)(160 181)(161 182)
(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)
(1 103)(2 102)(3 101)(4 100)(5 99)(6 98)(7 97)(8 96)(9 95)(10 94)(11 93)(12 115)(13 114)(14 113)(15 112)(16 111)(17 110)(18 109)(19 108)(20 107)(21 106)(22 105)(23 104)(24 126)(25 125)(26 124)(27 123)(28 122)(29 121)(30 120)(31 119)(32 118)(33 117)(34 116)(35 138)(36 137)(37 136)(38 135)(39 134)(40 133)(41 132)(42 131)(43 130)(44 129)(45 128)(46 127)(47 158)(48 157)(49 156)(50 155)(51 154)(52 153)(53 152)(54 151)(55 150)(56 149)(57 148)(58 147)(59 146)(60 145)(61 144)(62 143)(63 142)(64 141)(65 140)(66 139)(67 161)(68 160)(69 159)(70 179)(71 178)(72 177)(73 176)(74 175)(75 174)(76 173)(77 172)(78 171)(79 170)(80 169)(81 168)(82 167)(83 166)(84 165)(85 164)(86 163)(87 162)(88 184)(89 183)(90 182)(91 181)(92 180)
G:=sub<Sym(184)| (1,104)(2,105)(3,106)(4,107)(5,108)(6,109)(7,110)(8,111)(9,112)(10,113)(11,114)(12,115)(13,93)(14,94)(15,95)(16,96)(17,97)(18,98)(19,99)(20,100)(21,101)(22,102)(23,103)(24,122)(25,123)(26,124)(27,125)(28,126)(29,127)(30,128)(31,129)(32,130)(33,131)(34,132)(35,133)(36,134)(37,135)(38,136)(39,137)(40,138)(41,116)(42,117)(43,118)(44,119)(45,120)(46,121)(47,148)(48,149)(49,150)(50,151)(51,152)(52,153)(53,154)(54,155)(55,156)(56,157)(57,158)(58,159)(59,160)(60,161)(61,139)(62,140)(63,141)(64,142)(65,143)(66,144)(67,145)(68,146)(69,147)(70,169)(71,170)(72,171)(73,172)(74,173)(75,174)(76,175)(77,176)(78,177)(79,178)(80,179)(81,180)(82,181)(83,182)(84,183)(85,184)(86,162)(87,163)(88,164)(89,165)(90,166)(91,167)(92,168), (1,87)(2,88)(3,89)(4,90)(5,91)(6,92)(7,70)(8,71)(9,72)(10,73)(11,74)(12,75)(13,76)(14,77)(15,78)(16,79)(17,80)(18,81)(19,82)(20,83)(21,84)(22,85)(23,86)(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)(44,47)(45,48)(46,49)(93,175)(94,176)(95,177)(96,178)(97,179)(98,180)(99,181)(100,182)(101,183)(102,184)(103,162)(104,163)(105,164)(106,165)(107,166)(108,167)(109,168)(110,169)(111,170)(112,171)(113,172)(114,173)(115,174)(116,145)(117,146)(118,147)(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,139)(134,140)(135,141)(136,142)(137,143)(138,144), (1,38)(2,39)(3,40)(4,41)(5,42)(6,43)(7,44)(8,45)(9,46)(10,24)(11,25)(12,26)(13,27)(14,28)(15,29)(16,30)(17,31)(18,32)(19,33)(20,34)(21,35)(22,36)(23,37)(47,70)(48,71)(49,72)(50,73)(51,74)(52,75)(53,76)(54,77)(55,78)(56,79)(57,80)(58,81)(59,82)(60,83)(61,84)(62,85)(63,86)(64,87)(65,88)(66,89)(67,90)(68,91)(69,92)(93,125)(94,126)(95,127)(96,128)(97,129)(98,130)(99,131)(100,132)(101,133)(102,134)(103,135)(104,136)(105,137)(106,138)(107,116)(108,117)(109,118)(110,119)(111,120)(112,121)(113,122)(114,123)(115,124)(139,183)(140,184)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168)(148,169)(149,170)(150,171)(151,172)(152,173)(153,174)(154,175)(155,176)(156,177)(157,178)(158,179)(159,180)(160,181)(161,182), (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), (1,103)(2,102)(3,101)(4,100)(5,99)(6,98)(7,97)(8,96)(9,95)(10,94)(11,93)(12,115)(13,114)(14,113)(15,112)(16,111)(17,110)(18,109)(19,108)(20,107)(21,106)(22,105)(23,104)(24,126)(25,125)(26,124)(27,123)(28,122)(29,121)(30,120)(31,119)(32,118)(33,117)(34,116)(35,138)(36,137)(37,136)(38,135)(39,134)(40,133)(41,132)(42,131)(43,130)(44,129)(45,128)(46,127)(47,158)(48,157)(49,156)(50,155)(51,154)(52,153)(53,152)(54,151)(55,150)(56,149)(57,148)(58,147)(59,146)(60,145)(61,144)(62,143)(63,142)(64,141)(65,140)(66,139)(67,161)(68,160)(69,159)(70,179)(71,178)(72,177)(73,176)(74,175)(75,174)(76,173)(77,172)(78,171)(79,170)(80,169)(81,168)(82,167)(83,166)(84,165)(85,164)(86,163)(87,162)(88,184)(89,183)(90,182)(91,181)(92,180)>;
G:=Group( (1,104)(2,105)(3,106)(4,107)(5,108)(6,109)(7,110)(8,111)(9,112)(10,113)(11,114)(12,115)(13,93)(14,94)(15,95)(16,96)(17,97)(18,98)(19,99)(20,100)(21,101)(22,102)(23,103)(24,122)(25,123)(26,124)(27,125)(28,126)(29,127)(30,128)(31,129)(32,130)(33,131)(34,132)(35,133)(36,134)(37,135)(38,136)(39,137)(40,138)(41,116)(42,117)(43,118)(44,119)(45,120)(46,121)(47,148)(48,149)(49,150)(50,151)(51,152)(52,153)(53,154)(54,155)(55,156)(56,157)(57,158)(58,159)(59,160)(60,161)(61,139)(62,140)(63,141)(64,142)(65,143)(66,144)(67,145)(68,146)(69,147)(70,169)(71,170)(72,171)(73,172)(74,173)(75,174)(76,175)(77,176)(78,177)(79,178)(80,179)(81,180)(82,181)(83,182)(84,183)(85,184)(86,162)(87,163)(88,164)(89,165)(90,166)(91,167)(92,168), (1,87)(2,88)(3,89)(4,90)(5,91)(6,92)(7,70)(8,71)(9,72)(10,73)(11,74)(12,75)(13,76)(14,77)(15,78)(16,79)(17,80)(18,81)(19,82)(20,83)(21,84)(22,85)(23,86)(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)(44,47)(45,48)(46,49)(93,175)(94,176)(95,177)(96,178)(97,179)(98,180)(99,181)(100,182)(101,183)(102,184)(103,162)(104,163)(105,164)(106,165)(107,166)(108,167)(109,168)(110,169)(111,170)(112,171)(113,172)(114,173)(115,174)(116,145)(117,146)(118,147)(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,139)(134,140)(135,141)(136,142)(137,143)(138,144), (1,38)(2,39)(3,40)(4,41)(5,42)(6,43)(7,44)(8,45)(9,46)(10,24)(11,25)(12,26)(13,27)(14,28)(15,29)(16,30)(17,31)(18,32)(19,33)(20,34)(21,35)(22,36)(23,37)(47,70)(48,71)(49,72)(50,73)(51,74)(52,75)(53,76)(54,77)(55,78)(56,79)(57,80)(58,81)(59,82)(60,83)(61,84)(62,85)(63,86)(64,87)(65,88)(66,89)(67,90)(68,91)(69,92)(93,125)(94,126)(95,127)(96,128)(97,129)(98,130)(99,131)(100,132)(101,133)(102,134)(103,135)(104,136)(105,137)(106,138)(107,116)(108,117)(109,118)(110,119)(111,120)(112,121)(113,122)(114,123)(115,124)(139,183)(140,184)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168)(148,169)(149,170)(150,171)(151,172)(152,173)(153,174)(154,175)(155,176)(156,177)(157,178)(158,179)(159,180)(160,181)(161,182), (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), (1,103)(2,102)(3,101)(4,100)(5,99)(6,98)(7,97)(8,96)(9,95)(10,94)(11,93)(12,115)(13,114)(14,113)(15,112)(16,111)(17,110)(18,109)(19,108)(20,107)(21,106)(22,105)(23,104)(24,126)(25,125)(26,124)(27,123)(28,122)(29,121)(30,120)(31,119)(32,118)(33,117)(34,116)(35,138)(36,137)(37,136)(38,135)(39,134)(40,133)(41,132)(42,131)(43,130)(44,129)(45,128)(46,127)(47,158)(48,157)(49,156)(50,155)(51,154)(52,153)(53,152)(54,151)(55,150)(56,149)(57,148)(58,147)(59,146)(60,145)(61,144)(62,143)(63,142)(64,141)(65,140)(66,139)(67,161)(68,160)(69,159)(70,179)(71,178)(72,177)(73,176)(74,175)(75,174)(76,173)(77,172)(78,171)(79,170)(80,169)(81,168)(82,167)(83,166)(84,165)(85,164)(86,163)(87,162)(88,184)(89,183)(90,182)(91,181)(92,180) );
G=PermutationGroup([[(1,104),(2,105),(3,106),(4,107),(5,108),(6,109),(7,110),(8,111),(9,112),(10,113),(11,114),(12,115),(13,93),(14,94),(15,95),(16,96),(17,97),(18,98),(19,99),(20,100),(21,101),(22,102),(23,103),(24,122),(25,123),(26,124),(27,125),(28,126),(29,127),(30,128),(31,129),(32,130),(33,131),(34,132),(35,133),(36,134),(37,135),(38,136),(39,137),(40,138),(41,116),(42,117),(43,118),(44,119),(45,120),(46,121),(47,148),(48,149),(49,150),(50,151),(51,152),(52,153),(53,154),(54,155),(55,156),(56,157),(57,158),(58,159),(59,160),(60,161),(61,139),(62,140),(63,141),(64,142),(65,143),(66,144),(67,145),(68,146),(69,147),(70,169),(71,170),(72,171),(73,172),(74,173),(75,174),(76,175),(77,176),(78,177),(79,178),(80,179),(81,180),(82,181),(83,182),(84,183),(85,184),(86,162),(87,163),(88,164),(89,165),(90,166),(91,167),(92,168)], [(1,87),(2,88),(3,89),(4,90),(5,91),(6,92),(7,70),(8,71),(9,72),(10,73),(11,74),(12,75),(13,76),(14,77),(15,78),(16,79),(17,80),(18,81),(19,82),(20,83),(21,84),(22,85),(23,86),(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),(44,47),(45,48),(46,49),(93,175),(94,176),(95,177),(96,178),(97,179),(98,180),(99,181),(100,182),(101,183),(102,184),(103,162),(104,163),(105,164),(106,165),(107,166),(108,167),(109,168),(110,169),(111,170),(112,171),(113,172),(114,173),(115,174),(116,145),(117,146),(118,147),(119,148),(120,149),(121,150),(122,151),(123,152),(124,153),(125,154),(126,155),(127,156),(128,157),(129,158),(130,159),(131,160),(132,161),(133,139),(134,140),(135,141),(136,142),(137,143),(138,144)], [(1,38),(2,39),(3,40),(4,41),(5,42),(6,43),(7,44),(8,45),(9,46),(10,24),(11,25),(12,26),(13,27),(14,28),(15,29),(16,30),(17,31),(18,32),(19,33),(20,34),(21,35),(22,36),(23,37),(47,70),(48,71),(49,72),(50,73),(51,74),(52,75),(53,76),(54,77),(55,78),(56,79),(57,80),(58,81),(59,82),(60,83),(61,84),(62,85),(63,86),(64,87),(65,88),(66,89),(67,90),(68,91),(69,92),(93,125),(94,126),(95,127),(96,128),(97,129),(98,130),(99,131),(100,132),(101,133),(102,134),(103,135),(104,136),(105,137),(106,138),(107,116),(108,117),(109,118),(110,119),(111,120),(112,121),(113,122),(114,123),(115,124),(139,183),(140,184),(141,162),(142,163),(143,164),(144,165),(145,166),(146,167),(147,168),(148,169),(149,170),(150,171),(151,172),(152,173),(153,174),(154,175),(155,176),(156,177),(157,178),(158,179),(159,180),(160,181),(161,182)], [(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)], [(1,103),(2,102),(3,101),(4,100),(5,99),(6,98),(7,97),(8,96),(9,95),(10,94),(11,93),(12,115),(13,114),(14,113),(15,112),(16,111),(17,110),(18,109),(19,108),(20,107),(21,106),(22,105),(23,104),(24,126),(25,125),(26,124),(27,123),(28,122),(29,121),(30,120),(31,119),(32,118),(33,117),(34,116),(35,138),(36,137),(37,136),(38,135),(39,134),(40,133),(41,132),(42,131),(43,130),(44,129),(45,128),(46,127),(47,158),(48,157),(49,156),(50,155),(51,154),(52,153),(53,152),(54,151),(55,150),(56,149),(57,148),(58,147),(59,146),(60,145),(61,144),(62,143),(63,142),(64,141),(65,140),(66,139),(67,161),(68,160),(69,159),(70,179),(71,178),(72,177),(73,176),(74,175),(75,174),(76,173),(77,172),(78,171),(79,170),(80,169),(81,168),(82,167),(83,166),(84,165),(85,164),(86,163),(87,162),(88,184),(89,183),(90,182),(91,181),(92,180)]])
104 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | ··· | 2O | 23A | ··· | 23K | 46A | ··· | 46BY |
| order | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 23 | ··· | 23 | 46 | ··· | 46 |
| size | 1 | 1 | ··· | 1 | 23 | ··· | 23 | 2 | ··· | 2 | 2 | ··· | 2 |
104 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | + | + |
| image | C1 | C2 | C2 | D23 | D46 |
| kernel | C23×D23 | C22×D23 | C22×C46 | C23 | C22 |
| # reps | 1 | 14 | 1 | 11 | 77 |
Matrix representation of C23×D23 ►in GL4(𝔽47) generated by
| 1 | 0 | 0 | 0 |
| 0 | 46 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 46 | 0 | 0 |
| 0 | 0 | 46 | 0 |
| 0 | 0 | 0 | 46 |
| 46 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 16 | 1 |
| 0 | 0 | 11 | 36 |
| 46 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 20 | 41 |
| 0 | 0 | 43 | 27 |
G:=sub<GL(4,GF(47))| [1,0,0,0,0,46,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,46,0,0,0,0,46,0,0,0,0,46],[46,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,16,11,0,0,1,36],[46,0,0,0,0,1,0,0,0,0,20,43,0,0,41,27] >;
C23×D23 in GAP, Magma, Sage, TeX
C_2^3\times D_{23} % in TeX
G:=Group("C2^3xD23"); // GroupNames label
G:=SmallGroup(368,41);
// by ID
G=gap.SmallGroup(368,41);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-23,8804]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^23=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e=d^-1>;
// generators/relations