metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23.46D20, (C2×C8).187D10, C20.415(C2×D4), (C2×C4).148D20, (C2×C20).166D4, (C2×Dic10)⋊25C4, C22.55(C2×D20), (C22×C10).99D4, C20.44D4⋊39C2, C20.71(C22⋊C4), C20.173(C22×C4), (C2×C20).771C23, (C2×C40).317C22, Dic10.40(C2×C4), C2.3(C8.D10), (C22×C4).132D10, C5⋊4(C23.38D4), (C2×M4(2)).14D5, C4.11(D10⋊C4), C10.19(C8.C22), (C10×M4(2)).25C2, C4⋊Dic5.283C22, (C22×C20).179C22, (C22×Dic10).15C2, C22.26(D10⋊C4), (C2×Dic10).226C22, C23.21D10.16C2, C4.72(C2×C4×D5), (C2×C4).48(C4×D5), C4.108(C2×C5⋊D4), (C2×C20).272(C2×C4), (C2×C10).161(C2×D4), (C2×C4).75(C5⋊D4), C10.95(C2×C22⋊C4), C2.26(C2×D10⋊C4), (C2×C4).719(C22×D5), (C2×C10).82(C22⋊C4), SmallGroup(320,747)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23.46D20
G = < a,b,c,d,e | a2=b2=c2=1, d20=e2=c, ab=ba, dad-1=ac=ca, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=bd19 >
Subgroups: 526 in 150 conjugacy classes, 63 normal (23 characteristic)
C1, C2, C2 [×2], C2 [×2], C4 [×2], C4 [×2], C4 [×6], C22, C22 [×2], C22 [×2], C5, C8 [×2], C2×C4 [×2], C2×C4 [×4], C2×C4 [×8], Q8 [×10], C23, C10, C10 [×2], C10 [×2], C42, C22⋊C4, C4⋊C4 [×2], C2×C8 [×2], M4(2) [×2], C22×C4, C22×C4, C2×Q8 [×9], Dic5 [×6], C20 [×2], C20 [×2], C2×C10, C2×C10 [×2], C2×C10 [×2], Q8⋊C4 [×4], C42⋊C2, C2×M4(2), C22×Q8, C40 [×2], Dic10 [×4], Dic10 [×6], C2×Dic5 [×8], C2×C20 [×2], C2×C20 [×4], C22×C10, C23.38D4, C4×Dic5, C4⋊Dic5 [×2], C23.D5, C2×C40 [×2], C5×M4(2) [×2], C2×Dic10 [×6], C2×Dic10 [×3], C22×Dic5, C22×C20, C20.44D4 [×4], C23.21D10, C10×M4(2), C22×Dic10, C23.46D20
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×4], C23, D5, C22⋊C4 [×4], C22×C4, C2×D4 [×2], D10 [×3], C2×C22⋊C4, C8.C22 [×2], C4×D5 [×2], D20 [×2], C5⋊D4 [×2], C22×D5, C23.38D4, D10⋊C4 [×4], C2×C4×D5, C2×D20, C2×C5⋊D4, C8.D10 [×2], C2×D10⋊C4, C23.46D20
►On 160 points
Generators in S160
(1 120)(2 101)(3 82)(4 103)(5 84)(6 105)(7 86)(8 107)(9 88)(10 109)(11 90)(12 111)(13 92)(14 113)(15 94)(16 115)(17 96)(18 117)(19 98)(20 119)(21 100)(22 81)(23 102)(24 83)(25 104)(26 85)(27 106)(28 87)(29 108)(30 89)(31 110)(32 91)(33 112)(34 93)(35 114)(36 95)(37 116)(38 97)(39 118)(40 99)(41 139)(42 160)(43 141)(44 122)(45 143)(46 124)(47 145)(48 126)(49 147)(50 128)(51 149)(52 130)(53 151)(54 132)(55 153)(56 134)(57 155)(58 136)(59 157)(60 138)(61 159)(62 140)(63 121)(64 142)(65 123)(66 144)(67 125)(68 146)(69 127)(70 148)(71 129)(72 150)(73 131)(74 152)(75 133)(76 154)(77 135)(78 156)(79 137)(80 158)
(1 120)(2 81)(3 82)(4 83)(5 84)(6 85)(7 86)(8 87)(9 88)(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)(41 159)(42 160)(43 121)(44 122)(45 123)(46 124)(47 125)(48 126)(49 127)(50 128)(51 129)(52 130)(53 131)(54 132)(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)
(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)
(1 160 21 140)(2 61 22 41)(3 158 23 138)(4 59 24 79)(5 156 25 136)(6 57 26 77)(7 154 27 134)(8 55 28 75)(9 152 29 132)(10 53 30 73)(11 150 31 130)(12 51 32 71)(13 148 33 128)(14 49 34 69)(15 146 35 126)(16 47 36 67)(17 144 37 124)(18 45 38 65)(19 142 39 122)(20 43 40 63)(42 100 62 120)(44 98 64 118)(46 96 66 116)(48 94 68 114)(50 92 70 112)(52 90 72 110)(54 88 74 108)(56 86 76 106)(58 84 78 104)(60 82 80 102)(81 139 101 159)(83 137 103 157)(85 135 105 155)(87 133 107 153)(89 131 109 151)(91 129 111 149)(93 127 113 147)(95 125 115 145)(97 123 117 143)(99 121 119 141)
G:=sub<Sym(160)| (1,120)(2,101)(3,82)(4,103)(5,84)(6,105)(7,86)(8,107)(9,88)(10,109)(11,90)(12,111)(13,92)(14,113)(15,94)(16,115)(17,96)(18,117)(19,98)(20,119)(21,100)(22,81)(23,102)(24,83)(25,104)(26,85)(27,106)(28,87)(29,108)(30,89)(31,110)(32,91)(33,112)(34,93)(35,114)(36,95)(37,116)(38,97)(39,118)(40,99)(41,139)(42,160)(43,141)(44,122)(45,143)(46,124)(47,145)(48,126)(49,147)(50,128)(51,149)(52,130)(53,151)(54,132)(55,153)(56,134)(57,155)(58,136)(59,157)(60,138)(61,159)(62,140)(63,121)(64,142)(65,123)(66,144)(67,125)(68,146)(69,127)(70,148)(71,129)(72,150)(73,131)(74,152)(75,133)(76,154)(77,135)(78,156)(79,137)(80,158), (1,120)(2,81)(3,82)(4,83)(5,84)(6,85)(7,86)(8,87)(9,88)(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)(41,159)(42,160)(43,121)(44,122)(45,123)(46,124)(47,125)(48,126)(49,127)(50,128)(51,129)(52,130)(53,131)(54,132)(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), (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), (1,160,21,140)(2,61,22,41)(3,158,23,138)(4,59,24,79)(5,156,25,136)(6,57,26,77)(7,154,27,134)(8,55,28,75)(9,152,29,132)(10,53,30,73)(11,150,31,130)(12,51,32,71)(13,148,33,128)(14,49,34,69)(15,146,35,126)(16,47,36,67)(17,144,37,124)(18,45,38,65)(19,142,39,122)(20,43,40,63)(42,100,62,120)(44,98,64,118)(46,96,66,116)(48,94,68,114)(50,92,70,112)(52,90,72,110)(54,88,74,108)(56,86,76,106)(58,84,78,104)(60,82,80,102)(81,139,101,159)(83,137,103,157)(85,135,105,155)(87,133,107,153)(89,131,109,151)(91,129,111,149)(93,127,113,147)(95,125,115,145)(97,123,117,143)(99,121,119,141)>;
G:=Group( (1,120)(2,101)(3,82)(4,103)(5,84)(6,105)(7,86)(8,107)(9,88)(10,109)(11,90)(12,111)(13,92)(14,113)(15,94)(16,115)(17,96)(18,117)(19,98)(20,119)(21,100)(22,81)(23,102)(24,83)(25,104)(26,85)(27,106)(28,87)(29,108)(30,89)(31,110)(32,91)(33,112)(34,93)(35,114)(36,95)(37,116)(38,97)(39,118)(40,99)(41,139)(42,160)(43,141)(44,122)(45,143)(46,124)(47,145)(48,126)(49,147)(50,128)(51,149)(52,130)(53,151)(54,132)(55,153)(56,134)(57,155)(58,136)(59,157)(60,138)(61,159)(62,140)(63,121)(64,142)(65,123)(66,144)(67,125)(68,146)(69,127)(70,148)(71,129)(72,150)(73,131)(74,152)(75,133)(76,154)(77,135)(78,156)(79,137)(80,158), (1,120)(2,81)(3,82)(4,83)(5,84)(6,85)(7,86)(8,87)(9,88)(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)(41,159)(42,160)(43,121)(44,122)(45,123)(46,124)(47,125)(48,126)(49,127)(50,128)(51,129)(52,130)(53,131)(54,132)(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), (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), (1,160,21,140)(2,61,22,41)(3,158,23,138)(4,59,24,79)(5,156,25,136)(6,57,26,77)(7,154,27,134)(8,55,28,75)(9,152,29,132)(10,53,30,73)(11,150,31,130)(12,51,32,71)(13,148,33,128)(14,49,34,69)(15,146,35,126)(16,47,36,67)(17,144,37,124)(18,45,38,65)(19,142,39,122)(20,43,40,63)(42,100,62,120)(44,98,64,118)(46,96,66,116)(48,94,68,114)(50,92,70,112)(52,90,72,110)(54,88,74,108)(56,86,76,106)(58,84,78,104)(60,82,80,102)(81,139,101,159)(83,137,103,157)(85,135,105,155)(87,133,107,153)(89,131,109,151)(91,129,111,149)(93,127,113,147)(95,125,115,145)(97,123,117,143)(99,121,119,141) );
G=PermutationGroup([(1,120),(2,101),(3,82),(4,103),(5,84),(6,105),(7,86),(8,107),(9,88),(10,109),(11,90),(12,111),(13,92),(14,113),(15,94),(16,115),(17,96),(18,117),(19,98),(20,119),(21,100),(22,81),(23,102),(24,83),(25,104),(26,85),(27,106),(28,87),(29,108),(30,89),(31,110),(32,91),(33,112),(34,93),(35,114),(36,95),(37,116),(38,97),(39,118),(40,99),(41,139),(42,160),(43,141),(44,122),(45,143),(46,124),(47,145),(48,126),(49,147),(50,128),(51,149),(52,130),(53,151),(54,132),(55,153),(56,134),(57,155),(58,136),(59,157),(60,138),(61,159),(62,140),(63,121),(64,142),(65,123),(66,144),(67,125),(68,146),(69,127),(70,148),(71,129),(72,150),(73,131),(74,152),(75,133),(76,154),(77,135),(78,156),(79,137),(80,158)], [(1,120),(2,81),(3,82),(4,83),(5,84),(6,85),(7,86),(8,87),(9,88),(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),(41,159),(42,160),(43,121),(44,122),(45,123),(46,124),(47,125),(48,126),(49,127),(50,128),(51,129),(52,130),(53,131),(54,132),(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)], [(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)], [(1,160,21,140),(2,61,22,41),(3,158,23,138),(4,59,24,79),(5,156,25,136),(6,57,26,77),(7,154,27,134),(8,55,28,75),(9,152,29,132),(10,53,30,73),(11,150,31,130),(12,51,32,71),(13,148,33,128),(14,49,34,69),(15,146,35,126),(16,47,36,67),(17,144,37,124),(18,45,38,65),(19,142,39,122),(20,43,40,63),(42,100,62,120),(44,98,64,118),(46,96,66,116),(48,94,68,114),(50,92,70,112),(52,90,72,110),(54,88,74,108),(56,86,76,106),(58,84,78,104),(60,82,80,102),(81,139,101,159),(83,137,103,157),(85,135,105,155),(87,133,107,153),(89,131,109,151),(91,129,111,149),(93,127,113,147),(95,125,115,145),(97,123,117,143),(99,121,119,141)])
62 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 5A | 5B | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 20A | ··· | 20H | 20I | 20J | 20K | 20L | 40A | ··· | 40P |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | 20 | 20 | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 20 | ··· | 20 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
62 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D5 | D10 | D10 | C4×D5 | D20 | C5⋊D4 | D20 | C8.C22 | C8.D10 |
| kernel | C23.46D20 | C20.44D4 | C23.21D10 | C10×M4(2) | C22×Dic10 | C2×Dic10 | C2×C20 | C22×C10 | C2×M4(2) | C2×C8 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C23 | C10 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 3 | 1 | 2 | 4 | 2 | 8 | 4 | 8 | 4 | 2 | 8 |
Matrix representation of C23.46D20 ►in GL6(𝔽41)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 9 | 0 | 0 | 0 | 0 |
| 32 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 40 | 34 |
| 0 | 0 | 9 | 11 | 0 | 0 |
| 0 | 0 | 30 | 14 | 0 | 0 |
| 6 | 3 | 0 | 0 | 0 | 0 |
| 2 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 22 | 0 | 0 |
| 0 | 0 | 32 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 38 |
| 0 | 0 | 0 | 0 | 17 | 38 |
G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[0,32,0,0,0,0,9,19,0,0,0,0,0,0,0,0,9,30,0,0,0,0,11,14,0,0,0,40,0,0,0,0,1,34,0,0],[6,2,0,0,0,0,3,35,0,0,0,0,0,0,22,32,0,0,0,0,22,19,0,0,0,0,0,0,3,17,0,0,0,0,38,38] >;
C23.46D20 in GAP, Magma, Sage, TeX
C_2^3._{46}D_{20} % in TeX
G:=Group("C2^3.46D20"); // GroupNames label
G:=SmallGroup(320,747);
// by ID
G=gap.SmallGroup(320,747);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,232,254,387,142,1123,136,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=1,d^20=e^2=c,a*b=b*a,d*a*d^-1=a*c=c*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^-1=b*d^19>;
// generators/relations