metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23.23D22, D22⋊C4⋊2C2, (C22×C44)⋊2C2, (C2×C4).65D22, C22.42(C2×D4), (C2×C22).37D4, (C22×C4)⋊3D11, Dic11⋊C4⋊3C2, C23.D11⋊6C2, C22.18(C4○D4), (C2×C22).47C23, (C2×C44).78C22, C22.9(C11⋊D4), C11⋊4(C22.D4), C2.18(D44⋊5C2), (C22×C22).39C22, (C22×D11).9C22, C22.55(C22×D11), (C2×Dic11).15C22, C2.6(C2×C11⋊D4), (C2×C11⋊D4).6C2, SmallGroup(352,124)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23.23D22
G = < a,b,c,d,e | a2=b2=c2=1, d22=c, e2=cb=bc, ab=ba, eae-1=ac=ca, ad=da, bd=db, be=eb, cd=dc, ce=ec, ede-1=bd21 >
Subgroups: 426 in 78 conjugacy classes, 33 normal (15 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C2×C4, C2×C4, D4, C23, C23, C11, C22⋊C4, C4⋊C4, C22×C4, C2×D4, D11, C22, C22, C22, C22.D4, Dic11, C44, D22, C2×C22, C2×C22, C2×C22, C2×Dic11, C2×Dic11, C11⋊D4, C2×C44, C2×C44, C22×D11, C22×C22, Dic11⋊C4, D22⋊C4, C23.D11, C2×C11⋊D4, C22×C44, C23.23D22
Quotients: C1, C2, C22, D4, C23, C2×D4, C4○D4, D11, C22.D4, D22, C11⋊D4, C22×D11, D44⋊5C2, C2×C11⋊D4, C23.23D22
►On 176 points
Generators in S176
(1 124)(2 125)(3 126)(4 127)(5 128)(6 129)(7 130)(8 131)(9 132)(10 89)(11 90)(12 91)(13 92)(14 93)(15 94)(16 95)(17 96)(18 97)(19 98)(20 99)(21 100)(22 101)(23 102)(24 103)(25 104)(26 105)(27 106)(28 107)(29 108)(30 109)(31 110)(32 111)(33 112)(34 113)(35 114)(36 115)(37 116)(38 117)(39 118)(40 119)(41 120)(42 121)(43 122)(44 123)(45 167)(46 168)(47 169)(48 170)(49 171)(50 172)(51 173)(52 174)(53 175)(54 176)(55 133)(56 134)(57 135)(58 136)(59 137)(60 138)(61 139)(62 140)(63 141)(64 142)(65 143)(66 144)(67 145)(68 146)(69 147)(70 148)(71 149)(72 150)(73 151)(74 152)(75 153)(76 154)(77 155)(78 156)(79 157)(80 158)(81 159)(82 160)(83 161)(84 162)(85 163)(86 164)(87 165)(88 166)
(1 135)(2 136)(3 137)(4 138)(5 139)(6 140)(7 141)(8 142)(9 143)(10 144)(11 145)(12 146)(13 147)(14 148)(15 149)(16 150)(17 151)(18 152)(19 153)(20 154)(21 155)(22 156)(23 157)(24 158)(25 159)(26 160)(27 161)(28 162)(29 163)(30 164)(31 165)(32 166)(33 167)(34 168)(35 169)(36 170)(37 171)(38 172)(39 173)(40 174)(41 175)(42 176)(43 133)(44 134)(45 112)(46 113)(47 114)(48 115)(49 116)(50 117)(51 118)(52 119)(53 120)(54 121)(55 122)(56 123)(57 124)(58 125)(59 126)(60 127)(61 128)(62 129)(63 130)(64 131)(65 132)(66 89)(67 90)(68 91)(69 92)(70 93)(71 94)(72 95)(73 96)(74 97)(75 98)(76 99)(77 100)(78 101)(79 102)(80 103)(81 104)(82 105)(83 106)(84 107)(85 108)(86 109)(87 110)(88 111)
(1 23)(2 24)(3 25)(4 26)(5 27)(6 28)(7 29)(8 30)(9 31)(10 32)(11 33)(12 34)(13 35)(14 36)(15 37)(16 38)(17 39)(18 40)(19 41)(20 42)(21 43)(22 44)(45 67)(46 68)(47 69)(48 70)(49 71)(50 72)(51 73)(52 74)(53 75)(54 76)(55 77)(56 78)(57 79)(58 80)(59 81)(60 82)(61 83)(62 84)(63 85)(64 86)(65 87)(66 88)(89 111)(90 112)(91 113)(92 114)(93 115)(94 116)(95 117)(96 118)(97 119)(98 120)(99 121)(100 122)(101 123)(102 124)(103 125)(104 126)(105 127)(106 128)(107 129)(108 130)(109 131)(110 132)(133 155)(134 156)(135 157)(136 158)(137 159)(138 160)(139 161)(140 162)(141 163)(142 164)(143 165)(144 166)(145 167)(146 168)(147 169)(148 170)(149 171)(150 172)(151 173)(152 174)(153 175)(154 176)
(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)
(1 22 157 134)(2 133 158 21)(3 20 159 176)(4 175 160 19)(5 18 161 174)(6 173 162 17)(7 16 163 172)(8 171 164 15)(9 14 165 170)(10 169 166 13)(11 12 167 168)(23 44 135 156)(24 155 136 43)(25 42 137 154)(26 153 138 41)(27 40 139 152)(28 151 140 39)(29 38 141 150)(30 149 142 37)(31 36 143 148)(32 147 144 35)(33 34 145 146)(45 68 90 113)(46 112 91 67)(47 66 92 111)(48 110 93 65)(49 64 94 109)(50 108 95 63)(51 62 96 107)(52 106 97 61)(53 60 98 105)(54 104 99 59)(55 58 100 103)(56 102 101 57)(69 88 114 89)(70 132 115 87)(71 86 116 131)(72 130 117 85)(73 84 118 129)(74 128 119 83)(75 82 120 127)(76 126 121 81)(77 80 122 125)(78 124 123 79)
G:=sub<Sym(176)| (1,124)(2,125)(3,126)(4,127)(5,128)(6,129)(7,130)(8,131)(9,132)(10,89)(11,90)(12,91)(13,92)(14,93)(15,94)(16,95)(17,96)(18,97)(19,98)(20,99)(21,100)(22,101)(23,102)(24,103)(25,104)(26,105)(27,106)(28,107)(29,108)(30,109)(31,110)(32,111)(33,112)(34,113)(35,114)(36,115)(37,116)(38,117)(39,118)(40,119)(41,120)(42,121)(43,122)(44,123)(45,167)(46,168)(47,169)(48,170)(49,171)(50,172)(51,173)(52,174)(53,175)(54,176)(55,133)(56,134)(57,135)(58,136)(59,137)(60,138)(61,139)(62,140)(63,141)(64,142)(65,143)(66,144)(67,145)(68,146)(69,147)(70,148)(71,149)(72,150)(73,151)(74,152)(75,153)(76,154)(77,155)(78,156)(79,157)(80,158)(81,159)(82,160)(83,161)(84,162)(85,163)(86,164)(87,165)(88,166), (1,135)(2,136)(3,137)(4,138)(5,139)(6,140)(7,141)(8,142)(9,143)(10,144)(11,145)(12,146)(13,147)(14,148)(15,149)(16,150)(17,151)(18,152)(19,153)(20,154)(21,155)(22,156)(23,157)(24,158)(25,159)(26,160)(27,161)(28,162)(29,163)(30,164)(31,165)(32,166)(33,167)(34,168)(35,169)(36,170)(37,171)(38,172)(39,173)(40,174)(41,175)(42,176)(43,133)(44,134)(45,112)(46,113)(47,114)(48,115)(49,116)(50,117)(51,118)(52,119)(53,120)(54,121)(55,122)(56,123)(57,124)(58,125)(59,126)(60,127)(61,128)(62,129)(63,130)(64,131)(65,132)(66,89)(67,90)(68,91)(69,92)(70,93)(71,94)(72,95)(73,96)(74,97)(75,98)(76,99)(77,100)(78,101)(79,102)(80,103)(81,104)(82,105)(83,106)(84,107)(85,108)(86,109)(87,110)(88,111), (1,23)(2,24)(3,25)(4,26)(5,27)(6,28)(7,29)(8,30)(9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(45,67)(46,68)(47,69)(48,70)(49,71)(50,72)(51,73)(52,74)(53,75)(54,76)(55,77)(56,78)(57,79)(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88)(89,111)(90,112)(91,113)(92,114)(93,115)(94,116)(95,117)(96,118)(97,119)(98,120)(99,121)(100,122)(101,123)(102,124)(103,125)(104,126)(105,127)(106,128)(107,129)(108,130)(109,131)(110,132)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)(141,163)(142,164)(143,165)(144,166)(145,167)(146,168)(147,169)(148,170)(149,171)(150,172)(151,173)(152,174)(153,175)(154,176), (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), (1,22,157,134)(2,133,158,21)(3,20,159,176)(4,175,160,19)(5,18,161,174)(6,173,162,17)(7,16,163,172)(8,171,164,15)(9,14,165,170)(10,169,166,13)(11,12,167,168)(23,44,135,156)(24,155,136,43)(25,42,137,154)(26,153,138,41)(27,40,139,152)(28,151,140,39)(29,38,141,150)(30,149,142,37)(31,36,143,148)(32,147,144,35)(33,34,145,146)(45,68,90,113)(46,112,91,67)(47,66,92,111)(48,110,93,65)(49,64,94,109)(50,108,95,63)(51,62,96,107)(52,106,97,61)(53,60,98,105)(54,104,99,59)(55,58,100,103)(56,102,101,57)(69,88,114,89)(70,132,115,87)(71,86,116,131)(72,130,117,85)(73,84,118,129)(74,128,119,83)(75,82,120,127)(76,126,121,81)(77,80,122,125)(78,124,123,79)>;
G:=Group( (1,124)(2,125)(3,126)(4,127)(5,128)(6,129)(7,130)(8,131)(9,132)(10,89)(11,90)(12,91)(13,92)(14,93)(15,94)(16,95)(17,96)(18,97)(19,98)(20,99)(21,100)(22,101)(23,102)(24,103)(25,104)(26,105)(27,106)(28,107)(29,108)(30,109)(31,110)(32,111)(33,112)(34,113)(35,114)(36,115)(37,116)(38,117)(39,118)(40,119)(41,120)(42,121)(43,122)(44,123)(45,167)(46,168)(47,169)(48,170)(49,171)(50,172)(51,173)(52,174)(53,175)(54,176)(55,133)(56,134)(57,135)(58,136)(59,137)(60,138)(61,139)(62,140)(63,141)(64,142)(65,143)(66,144)(67,145)(68,146)(69,147)(70,148)(71,149)(72,150)(73,151)(74,152)(75,153)(76,154)(77,155)(78,156)(79,157)(80,158)(81,159)(82,160)(83,161)(84,162)(85,163)(86,164)(87,165)(88,166), (1,135)(2,136)(3,137)(4,138)(5,139)(6,140)(7,141)(8,142)(9,143)(10,144)(11,145)(12,146)(13,147)(14,148)(15,149)(16,150)(17,151)(18,152)(19,153)(20,154)(21,155)(22,156)(23,157)(24,158)(25,159)(26,160)(27,161)(28,162)(29,163)(30,164)(31,165)(32,166)(33,167)(34,168)(35,169)(36,170)(37,171)(38,172)(39,173)(40,174)(41,175)(42,176)(43,133)(44,134)(45,112)(46,113)(47,114)(48,115)(49,116)(50,117)(51,118)(52,119)(53,120)(54,121)(55,122)(56,123)(57,124)(58,125)(59,126)(60,127)(61,128)(62,129)(63,130)(64,131)(65,132)(66,89)(67,90)(68,91)(69,92)(70,93)(71,94)(72,95)(73,96)(74,97)(75,98)(76,99)(77,100)(78,101)(79,102)(80,103)(81,104)(82,105)(83,106)(84,107)(85,108)(86,109)(87,110)(88,111), (1,23)(2,24)(3,25)(4,26)(5,27)(6,28)(7,29)(8,30)(9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(45,67)(46,68)(47,69)(48,70)(49,71)(50,72)(51,73)(52,74)(53,75)(54,76)(55,77)(56,78)(57,79)(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88)(89,111)(90,112)(91,113)(92,114)(93,115)(94,116)(95,117)(96,118)(97,119)(98,120)(99,121)(100,122)(101,123)(102,124)(103,125)(104,126)(105,127)(106,128)(107,129)(108,130)(109,131)(110,132)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)(141,163)(142,164)(143,165)(144,166)(145,167)(146,168)(147,169)(148,170)(149,171)(150,172)(151,173)(152,174)(153,175)(154,176), (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), (1,22,157,134)(2,133,158,21)(3,20,159,176)(4,175,160,19)(5,18,161,174)(6,173,162,17)(7,16,163,172)(8,171,164,15)(9,14,165,170)(10,169,166,13)(11,12,167,168)(23,44,135,156)(24,155,136,43)(25,42,137,154)(26,153,138,41)(27,40,139,152)(28,151,140,39)(29,38,141,150)(30,149,142,37)(31,36,143,148)(32,147,144,35)(33,34,145,146)(45,68,90,113)(46,112,91,67)(47,66,92,111)(48,110,93,65)(49,64,94,109)(50,108,95,63)(51,62,96,107)(52,106,97,61)(53,60,98,105)(54,104,99,59)(55,58,100,103)(56,102,101,57)(69,88,114,89)(70,132,115,87)(71,86,116,131)(72,130,117,85)(73,84,118,129)(74,128,119,83)(75,82,120,127)(76,126,121,81)(77,80,122,125)(78,124,123,79) );
G=PermutationGroup([[(1,124),(2,125),(3,126),(4,127),(5,128),(6,129),(7,130),(8,131),(9,132),(10,89),(11,90),(12,91),(13,92),(14,93),(15,94),(16,95),(17,96),(18,97),(19,98),(20,99),(21,100),(22,101),(23,102),(24,103),(25,104),(26,105),(27,106),(28,107),(29,108),(30,109),(31,110),(32,111),(33,112),(34,113),(35,114),(36,115),(37,116),(38,117),(39,118),(40,119),(41,120),(42,121),(43,122),(44,123),(45,167),(46,168),(47,169),(48,170),(49,171),(50,172),(51,173),(52,174),(53,175),(54,176),(55,133),(56,134),(57,135),(58,136),(59,137),(60,138),(61,139),(62,140),(63,141),(64,142),(65,143),(66,144),(67,145),(68,146),(69,147),(70,148),(71,149),(72,150),(73,151),(74,152),(75,153),(76,154),(77,155),(78,156),(79,157),(80,158),(81,159),(82,160),(83,161),(84,162),(85,163),(86,164),(87,165),(88,166)], [(1,135),(2,136),(3,137),(4,138),(5,139),(6,140),(7,141),(8,142),(9,143),(10,144),(11,145),(12,146),(13,147),(14,148),(15,149),(16,150),(17,151),(18,152),(19,153),(20,154),(21,155),(22,156),(23,157),(24,158),(25,159),(26,160),(27,161),(28,162),(29,163),(30,164),(31,165),(32,166),(33,167),(34,168),(35,169),(36,170),(37,171),(38,172),(39,173),(40,174),(41,175),(42,176),(43,133),(44,134),(45,112),(46,113),(47,114),(48,115),(49,116),(50,117),(51,118),(52,119),(53,120),(54,121),(55,122),(56,123),(57,124),(58,125),(59,126),(60,127),(61,128),(62,129),(63,130),(64,131),(65,132),(66,89),(67,90),(68,91),(69,92),(70,93),(71,94),(72,95),(73,96),(74,97),(75,98),(76,99),(77,100),(78,101),(79,102),(80,103),(81,104),(82,105),(83,106),(84,107),(85,108),(86,109),(87,110),(88,111)], [(1,23),(2,24),(3,25),(4,26),(5,27),(6,28),(7,29),(8,30),(9,31),(10,32),(11,33),(12,34),(13,35),(14,36),(15,37),(16,38),(17,39),(18,40),(19,41),(20,42),(21,43),(22,44),(45,67),(46,68),(47,69),(48,70),(49,71),(50,72),(51,73),(52,74),(53,75),(54,76),(55,77),(56,78),(57,79),(58,80),(59,81),(60,82),(61,83),(62,84),(63,85),(64,86),(65,87),(66,88),(89,111),(90,112),(91,113),(92,114),(93,115),(94,116),(95,117),(96,118),(97,119),(98,120),(99,121),(100,122),(101,123),(102,124),(103,125),(104,126),(105,127),(106,128),(107,129),(108,130),(109,131),(110,132),(133,155),(134,156),(135,157),(136,158),(137,159),(138,160),(139,161),(140,162),(141,163),(142,164),(143,165),(144,166),(145,167),(146,168),(147,169),(148,170),(149,171),(150,172),(151,173),(152,174),(153,175),(154,176)], [(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)], [(1,22,157,134),(2,133,158,21),(3,20,159,176),(4,175,160,19),(5,18,161,174),(6,173,162,17),(7,16,163,172),(8,171,164,15),(9,14,165,170),(10,169,166,13),(11,12,167,168),(23,44,135,156),(24,155,136,43),(25,42,137,154),(26,153,138,41),(27,40,139,152),(28,151,140,39),(29,38,141,150),(30,149,142,37),(31,36,143,148),(32,147,144,35),(33,34,145,146),(45,68,90,113),(46,112,91,67),(47,66,92,111),(48,110,93,65),(49,64,94,109),(50,108,95,63),(51,62,96,107),(52,106,97,61),(53,60,98,105),(54,104,99,59),(55,58,100,103),(56,102,101,57),(69,88,114,89),(70,132,115,87),(71,86,116,131),(72,130,117,85),(73,84,118,129),(74,128,119,83),(75,82,120,127),(76,126,121,81),(77,80,122,125),(78,124,123,79)]])
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 11A | ··· | 11E | 22A | ··· | 22AI | 44A | ··· | 44AN |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 44 | 2 | 2 | 2 | 2 | 44 | 44 | 44 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | C4○D4 | D11 | D22 | D22 | C11⋊D4 | D44⋊5C2 |
| kernel | C23.23D22 | Dic11⋊C4 | D22⋊C4 | C23.D11 | C2×C11⋊D4 | C22×C44 | C2×C22 | C22 | C22×C4 | C2×C4 | C23 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 2 | 4 | 5 | 10 | 5 | 20 | 40 |
Matrix representation of C23.23D22 ►in GL4(𝔽89) generated by
| 3 | 50 | 0 | 0 |
| 39 | 86 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 88 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 88 | 0 |
| 0 | 0 | 0 | 88 |
| 88 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 58 | 31 | 0 | 0 |
| 58 | 8 | 0 | 0 |
| 0 | 0 | 27 | 25 |
| 0 | 0 | 36 | 30 |
| 31 | 58 | 0 | 0 |
| 8 | 58 | 0 | 0 |
| 0 | 0 | 60 | 77 |
| 0 | 0 | 85 | 29 |
G:=sub<GL(4,GF(89))| [3,39,0,0,50,86,0,0,0,0,1,0,0,0,0,1],[88,0,0,0,0,88,0,0,0,0,88,0,0,0,0,88],[88,0,0,0,0,88,0,0,0,0,1,0,0,0,0,1],[58,58,0,0,31,8,0,0,0,0,27,36,0,0,25,30],[31,8,0,0,58,58,0,0,0,0,60,85,0,0,77,29] >;
C23.23D22 in GAP, Magma, Sage, TeX
C_2^3._{23}D_{22} % in TeX
G:=Group("C2^3.23D22"); // GroupNames label
G:=SmallGroup(352,124);
// by ID
G=gap.SmallGroup(352,124);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,217,218,86,11525]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=1,d^22=c,e^2=c*b=b*c,a*b=b*a,e*a*e^-1=a*c=c*a,a*d=d*a,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=b*d^21>;
// generators/relations