metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23.23D20, C4○D20⋊8C4, (C22×C8)⋊5D5, (C22×C40)⋊4C2, D20.37(C2×C4), C20.411(C2×D4), (C2×C20).403D4, (C2×C4).172D20, (C2×C8).295D10, D20⋊5C4⋊44C2, C10.16(C4○D8), C22.54(C2×D20), C2.5(D40⋊7C2), C20.44D4⋊44C2, (C2×C40).356C22, (C2×C20).767C23, C20.172(C22×C4), Dic10.39(C2×C4), (C22×C4).429D10, (C22×C10).139D4, C5⋊5(C23.24D4), C4.55(D10⋊C4), C20.113(C22⋊C4), (C2×D20).205C22, C23.21D10⋊2C2, C4⋊Dic5.282C22, C22.6(D10⋊C4), (C22×C20).542C22, (C2×Dic10).225C22, C4.71(C2×C4×D5), (C2×C4○D20).5C2, (C2×C4).117(C4×D5), C4.104(C2×C5⋊D4), (C2×C20).408(C2×C4), (C2×C10).157(C2×D4), C10.94(C2×C22⋊C4), C2.25(C2×D10⋊C4), (C2×C4).255(C5⋊D4), (C2×C4).715(C22×D5), (C2×C10).128(C22⋊C4), SmallGroup(320,740)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23.23D20
G = < a,b,c,d,e | a2=b2=c2=1, d20=c, e2=cb=bc, ab=ba, eae-1=ac=ca, ad=da, bd=db, be=eb, cd=dc, ce=ec, ede-1=bd19 >
Subgroups: 622 in 158 conjugacy classes, 63 normal (25 characteristic)
C1, C2, C2, C2, C4, C4, C4, C22, C22, C22, C5, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D5, C10, C10, C10, C42, C22⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic5, C20, C20, D10, C2×C10, C2×C10, C2×C10, D4⋊C4, Q8⋊C4, C42⋊C2, C22×C8, C2×C4○D4, C40, Dic10, Dic10, C4×D5, D20, D20, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C22×D5, C22×C10, C23.24D4, C4×Dic5, C4⋊Dic5, C23.D5, C2×C40, C2×C40, C2×Dic10, C2×C4×D5, C2×D20, C4○D20, C4○D20, C2×C5⋊D4, C22×C20, C20.44D4, D20⋊5C4, C23.21D10, C22×C40, C2×C4○D20, C23.23D20
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D5, C22⋊C4, C22×C4, C2×D4, D10, C2×C22⋊C4, C4○D8, C4×D5, D20, C5⋊D4, C22×D5, C23.24D4, D10⋊C4, C2×C4×D5, C2×D20, C2×C5⋊D4, D40⋊7C2, C2×D10⋊C4, C23.23D20
►On 160 points
Generators in S160
(1 64)(2 65)(3 66)(4 67)(5 68)(6 69)(7 70)(8 71)(9 72)(10 73)(11 74)(12 75)(13 76)(14 77)(15 78)(16 79)(17 80)(18 41)(19 42)(20 43)(21 44)(22 45)(23 46)(24 47)(25 48)(26 49)(27 50)(28 51)(29 52)(30 53)(31 54)(32 55)(33 56)(34 57)(35 58)(36 59)(37 60)(38 61)(39 62)(40 63)(81 134)(82 135)(83 136)(84 137)(85 138)(86 139)(87 140)(88 141)(89 142)(90 143)(91 144)(92 145)(93 146)(94 147)(95 148)(96 149)(97 150)(98 151)(99 152)(100 153)(101 154)(102 155)(103 156)(104 157)(105 158)(106 159)(107 160)(108 121)(109 122)(110 123)(111 124)(112 125)(113 126)(114 127)(115 128)(116 129)(117 130)(118 131)(119 132)(120 133)
(1 112)(2 113)(3 114)(4 115)(5 116)(6 117)(7 118)(8 119)(9 120)(10 81)(11 82)(12 83)(13 84)(14 85)(15 86)(16 87)(17 88)(18 89)(19 90)(20 91)(21 92)(22 93)(23 94)(24 95)(25 96)(26 97)(27 98)(28 99)(29 100)(30 101)(31 102)(32 103)(33 104)(34 105)(35 106)(36 107)(37 108)(38 109)(39 110)(40 111)(41 142)(42 143)(43 144)(44 145)(45 146)(46 147)(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)(60 121)(61 122)(62 123)(63 124)(64 125)(65 126)(66 127)(67 128)(68 129)(69 130)(70 131)(71 132)(72 133)(73 134)(74 135)(75 136)(76 137)(77 138)(78 139)(79 140)(80 141)
(1 21)(2 22)(3 23)(4 24)(5 25)(6 26)(7 27)(8 28)(9 29)(10 30)(11 31)(12 32)(13 33)(14 34)(15 35)(16 36)(17 37)(18 38)(19 39)(20 40)(41 61)(42 62)(43 63)(44 64)(45 65)(46 66)(47 67)(48 68)(49 69)(50 70)(51 71)(52 72)(53 73)(54 74)(55 75)(56 76)(57 77)(58 78)(59 79)(60 80)(81 101)(82 102)(83 103)(84 104)(85 105)(86 106)(87 107)(88 108)(89 109)(90 110)(91 111)(92 112)(93 113)(94 114)(95 115)(96 116)(97 117)(98 118)(99 119)(100 120)(121 141)(122 142)(123 143)(124 144)(125 145)(126 146)(127 147)(128 148)(129 149)(130 150)(131 151)(132 152)(133 153)(134 154)(135 155)(136 156)(137 157)(138 158)(139 159)(140 160)
(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)
(1 91 92 40)(2 39 93 90)(3 89 94 38)(4 37 95 88)(5 87 96 36)(6 35 97 86)(7 85 98 34)(8 33 99 84)(9 83 100 32)(10 31 101 82)(11 81 102 30)(12 29 103 120)(13 119 104 28)(14 27 105 118)(15 117 106 26)(16 25 107 116)(17 115 108 24)(18 23 109 114)(19 113 110 22)(20 21 111 112)(41 66 122 147)(42 146 123 65)(43 64 124 145)(44 144 125 63)(45 62 126 143)(46 142 127 61)(47 60 128 141)(48 140 129 59)(49 58 130 139)(50 138 131 57)(51 56 132 137)(52 136 133 55)(53 54 134 135)(67 80 148 121)(68 160 149 79)(69 78 150 159)(70 158 151 77)(71 76 152 157)(72 156 153 75)(73 74 154 155)
G:=sub<Sym(160)| (1,64)(2,65)(3,66)(4,67)(5,68)(6,69)(7,70)(8,71)(9,72)(10,73)(11,74)(12,75)(13,76)(14,77)(15,78)(16,79)(17,80)(18,41)(19,42)(20,43)(21,44)(22,45)(23,46)(24,47)(25,48)(26,49)(27,50)(28,51)(29,52)(30,53)(31,54)(32,55)(33,56)(34,57)(35,58)(36,59)(37,60)(38,61)(39,62)(40,63)(81,134)(82,135)(83,136)(84,137)(85,138)(86,139)(87,140)(88,141)(89,142)(90,143)(91,144)(92,145)(93,146)(94,147)(95,148)(96,149)(97,150)(98,151)(99,152)(100,153)(101,154)(102,155)(103,156)(104,157)(105,158)(106,159)(107,160)(108,121)(109,122)(110,123)(111,124)(112,125)(113,126)(114,127)(115,128)(116,129)(117,130)(118,131)(119,132)(120,133), (1,112)(2,113)(3,114)(4,115)(5,116)(6,117)(7,118)(8,119)(9,120)(10,81)(11,82)(12,83)(13,84)(14,85)(15,86)(16,87)(17,88)(18,89)(19,90)(20,91)(21,92)(22,93)(23,94)(24,95)(25,96)(26,97)(27,98)(28,99)(29,100)(30,101)(31,102)(32,103)(33,104)(34,105)(35,106)(36,107)(37,108)(38,109)(39,110)(40,111)(41,142)(42,143)(43,144)(44,145)(45,146)(46,147)(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)(60,121)(61,122)(62,123)(63,124)(64,125)(65,126)(66,127)(67,128)(68,129)(69,130)(70,131)(71,132)(72,133)(73,134)(74,135)(75,136)(76,137)(77,138)(78,139)(79,140)(80,141), (1,21)(2,22)(3,23)(4,24)(5,25)(6,26)(7,27)(8,28)(9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(41,61)(42,62)(43,63)(44,64)(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,73)(54,74)(55,75)(56,76)(57,77)(58,78)(59,79)(60,80)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,113)(94,114)(95,115)(96,116)(97,117)(98,118)(99,119)(100,120)(121,141)(122,142)(123,143)(124,144)(125,145)(126,146)(127,147)(128,148)(129,149)(130,150)(131,151)(132,152)(133,153)(134,154)(135,155)(136,156)(137,157)(138,158)(139,159)(140,160), (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), (1,91,92,40)(2,39,93,90)(3,89,94,38)(4,37,95,88)(5,87,96,36)(6,35,97,86)(7,85,98,34)(8,33,99,84)(9,83,100,32)(10,31,101,82)(11,81,102,30)(12,29,103,120)(13,119,104,28)(14,27,105,118)(15,117,106,26)(16,25,107,116)(17,115,108,24)(18,23,109,114)(19,113,110,22)(20,21,111,112)(41,66,122,147)(42,146,123,65)(43,64,124,145)(44,144,125,63)(45,62,126,143)(46,142,127,61)(47,60,128,141)(48,140,129,59)(49,58,130,139)(50,138,131,57)(51,56,132,137)(52,136,133,55)(53,54,134,135)(67,80,148,121)(68,160,149,79)(69,78,150,159)(70,158,151,77)(71,76,152,157)(72,156,153,75)(73,74,154,155)>;
G:=Group( (1,64)(2,65)(3,66)(4,67)(5,68)(6,69)(7,70)(8,71)(9,72)(10,73)(11,74)(12,75)(13,76)(14,77)(15,78)(16,79)(17,80)(18,41)(19,42)(20,43)(21,44)(22,45)(23,46)(24,47)(25,48)(26,49)(27,50)(28,51)(29,52)(30,53)(31,54)(32,55)(33,56)(34,57)(35,58)(36,59)(37,60)(38,61)(39,62)(40,63)(81,134)(82,135)(83,136)(84,137)(85,138)(86,139)(87,140)(88,141)(89,142)(90,143)(91,144)(92,145)(93,146)(94,147)(95,148)(96,149)(97,150)(98,151)(99,152)(100,153)(101,154)(102,155)(103,156)(104,157)(105,158)(106,159)(107,160)(108,121)(109,122)(110,123)(111,124)(112,125)(113,126)(114,127)(115,128)(116,129)(117,130)(118,131)(119,132)(120,133), (1,112)(2,113)(3,114)(4,115)(5,116)(6,117)(7,118)(8,119)(9,120)(10,81)(11,82)(12,83)(13,84)(14,85)(15,86)(16,87)(17,88)(18,89)(19,90)(20,91)(21,92)(22,93)(23,94)(24,95)(25,96)(26,97)(27,98)(28,99)(29,100)(30,101)(31,102)(32,103)(33,104)(34,105)(35,106)(36,107)(37,108)(38,109)(39,110)(40,111)(41,142)(42,143)(43,144)(44,145)(45,146)(46,147)(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)(60,121)(61,122)(62,123)(63,124)(64,125)(65,126)(66,127)(67,128)(68,129)(69,130)(70,131)(71,132)(72,133)(73,134)(74,135)(75,136)(76,137)(77,138)(78,139)(79,140)(80,141), (1,21)(2,22)(3,23)(4,24)(5,25)(6,26)(7,27)(8,28)(9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(41,61)(42,62)(43,63)(44,64)(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,73)(54,74)(55,75)(56,76)(57,77)(58,78)(59,79)(60,80)(81,101)(82,102)(83,103)(84,104)(85,105)(86,106)(87,107)(88,108)(89,109)(90,110)(91,111)(92,112)(93,113)(94,114)(95,115)(96,116)(97,117)(98,118)(99,119)(100,120)(121,141)(122,142)(123,143)(124,144)(125,145)(126,146)(127,147)(128,148)(129,149)(130,150)(131,151)(132,152)(133,153)(134,154)(135,155)(136,156)(137,157)(138,158)(139,159)(140,160), (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), (1,91,92,40)(2,39,93,90)(3,89,94,38)(4,37,95,88)(5,87,96,36)(6,35,97,86)(7,85,98,34)(8,33,99,84)(9,83,100,32)(10,31,101,82)(11,81,102,30)(12,29,103,120)(13,119,104,28)(14,27,105,118)(15,117,106,26)(16,25,107,116)(17,115,108,24)(18,23,109,114)(19,113,110,22)(20,21,111,112)(41,66,122,147)(42,146,123,65)(43,64,124,145)(44,144,125,63)(45,62,126,143)(46,142,127,61)(47,60,128,141)(48,140,129,59)(49,58,130,139)(50,138,131,57)(51,56,132,137)(52,136,133,55)(53,54,134,135)(67,80,148,121)(68,160,149,79)(69,78,150,159)(70,158,151,77)(71,76,152,157)(72,156,153,75)(73,74,154,155) );
G=PermutationGroup([[(1,64),(2,65),(3,66),(4,67),(5,68),(6,69),(7,70),(8,71),(9,72),(10,73),(11,74),(12,75),(13,76),(14,77),(15,78),(16,79),(17,80),(18,41),(19,42),(20,43),(21,44),(22,45),(23,46),(24,47),(25,48),(26,49),(27,50),(28,51),(29,52),(30,53),(31,54),(32,55),(33,56),(34,57),(35,58),(36,59),(37,60),(38,61),(39,62),(40,63),(81,134),(82,135),(83,136),(84,137),(85,138),(86,139),(87,140),(88,141),(89,142),(90,143),(91,144),(92,145),(93,146),(94,147),(95,148),(96,149),(97,150),(98,151),(99,152),(100,153),(101,154),(102,155),(103,156),(104,157),(105,158),(106,159),(107,160),(108,121),(109,122),(110,123),(111,124),(112,125),(113,126),(114,127),(115,128),(116,129),(117,130),(118,131),(119,132),(120,133)], [(1,112),(2,113),(3,114),(4,115),(5,116),(6,117),(7,118),(8,119),(9,120),(10,81),(11,82),(12,83),(13,84),(14,85),(15,86),(16,87),(17,88),(18,89),(19,90),(20,91),(21,92),(22,93),(23,94),(24,95),(25,96),(26,97),(27,98),(28,99),(29,100),(30,101),(31,102),(32,103),(33,104),(34,105),(35,106),(36,107),(37,108),(38,109),(39,110),(40,111),(41,142),(42,143),(43,144),(44,145),(45,146),(46,147),(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),(60,121),(61,122),(62,123),(63,124),(64,125),(65,126),(66,127),(67,128),(68,129),(69,130),(70,131),(71,132),(72,133),(73,134),(74,135),(75,136),(76,137),(77,138),(78,139),(79,140),(80,141)], [(1,21),(2,22),(3,23),(4,24),(5,25),(6,26),(7,27),(8,28),(9,29),(10,30),(11,31),(12,32),(13,33),(14,34),(15,35),(16,36),(17,37),(18,38),(19,39),(20,40),(41,61),(42,62),(43,63),(44,64),(45,65),(46,66),(47,67),(48,68),(49,69),(50,70),(51,71),(52,72),(53,73),(54,74),(55,75),(56,76),(57,77),(58,78),(59,79),(60,80),(81,101),(82,102),(83,103),(84,104),(85,105),(86,106),(87,107),(88,108),(89,109),(90,110),(91,111),(92,112),(93,113),(94,114),(95,115),(96,116),(97,117),(98,118),(99,119),(100,120),(121,141),(122,142),(123,143),(124,144),(125,145),(126,146),(127,147),(128,148),(129,149),(130,150),(131,151),(132,152),(133,153),(134,154),(135,155),(136,156),(137,157),(138,158),(139,159),(140,160)], [(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)], [(1,91,92,40),(2,39,93,90),(3,89,94,38),(4,37,95,88),(5,87,96,36),(6,35,97,86),(7,85,98,34),(8,33,99,84),(9,83,100,32),(10,31,101,82),(11,81,102,30),(12,29,103,120),(13,119,104,28),(14,27,105,118),(15,117,106,26),(16,25,107,116),(17,115,108,24),(18,23,109,114),(19,113,110,22),(20,21,111,112),(41,66,122,147),(42,146,123,65),(43,64,124,145),(44,144,125,63),(45,62,126,143),(46,142,127,61),(47,60,128,141),(48,140,129,59),(49,58,130,139),(50,138,131,57),(51,56,132,137),(52,136,133,55),(53,54,134,135),(67,80,148,121),(68,160,149,79),(69,78,150,159),(70,158,151,77),(71,76,152,157),(72,156,153,75),(73,74,154,155)]])
92 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | ··· | 4L | 5A | 5B | 8A | ··· | 8H | 10A | ··· | 10N | 20A | ··· | 20P | 40A | ··· | 40AF |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 20 | 20 | 1 | 1 | 1 | 1 | 2 | 2 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
92 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D5 | D10 | D10 | C4○D8 | C4×D5 | D20 | C5⋊D4 | D20 | D40⋊7C2 |
| kernel | C23.23D20 | C20.44D4 | D20⋊5C4 | C23.21D10 | C22×C40 | C2×C4○D20 | C4○D20 | C2×C20 | C22×C10 | C22×C8 | C2×C8 | C22×C4 | C10 | C2×C4 | C2×C4 | C2×C4 | C23 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 8 | 3 | 1 | 2 | 4 | 2 | 8 | 8 | 4 | 8 | 4 | 32 |
Matrix representation of C23.23D20 ►in GL4(𝔽41) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 23 | 6 |
| 0 | 0 | 35 | 18 |
| 40 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 |
| 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 40 |
| 18 | 24 | 0 | 0 |
| 38 | 21 | 0 | 0 |
| 0 | 0 | 8 | 29 |
| 0 | 0 | 12 | 18 |
| 18 | 40 | 0 | 0 |
| 38 | 23 | 0 | 0 |
| 0 | 0 | 29 | 8 |
| 0 | 0 | 18 | 12 |
G:=sub<GL(4,GF(41))| [1,0,0,0,0,1,0,0,0,0,23,35,0,0,6,18],[40,0,0,0,0,40,0,0,0,0,40,0,0,0,0,40],[1,0,0,0,0,1,0,0,0,0,40,0,0,0,0,40],[18,38,0,0,24,21,0,0,0,0,8,12,0,0,29,18],[18,38,0,0,40,23,0,0,0,0,29,18,0,0,8,12] >;
C23.23D20 in GAP, Magma, Sage, TeX
C_2^3._{23}D_{20} % in TeX
G:=Group("C2^3.23D20"); // GroupNames label
G:=SmallGroup(320,740);
// by ID
G=gap.SmallGroup(320,740);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,254,142,1123,136,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=1,d^20=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^19>;
// generators/relations