metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23.46D20, (C2xC8).187D10, C20.415(C2xD4), (C2xC4).148D20, (C2xC20).166D4, (C2xDic10):25C4, C22.55(C2xD20), (C22xC10).99D4, C20.44D4:39C2, C20.71(C22:C4), C20.173(C22xC4), (C2xC20).771C23, (C2xC40).317C22, Dic10.40(C2xC4), C2.3(C8.D10), (C22xC4).132D10, C5:4(C23.38D4), (C2xM4(2)).14D5, C4.11(D10:C4), C10.19(C8.C22), (C10xM4(2)).25C2, C4:Dic5.283C22, (C22xC20).179C22, (C22xDic10).15C2, C22.26(D10:C4), (C2xDic10).226C22, C23.21D10.16C2, C4.72(C2xC4xD5), (C2xC4).48(C4xD5), C4.108(C2xC5:D4), (C2xC20).272(C2xC4), (C2xC10).161(C2xD4), (C2xC4).75(C5:D4), C10.95(C2xC22:C4), C2.26(C2xD10:C4), (C2xC4).719(C22xD5), (C2xC10).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, C2, C4, C4, C4, C22, C22, C22, C5, C8, C2xC4, C2xC4, C2xC4, Q8, C23, C10, C10, C10, C42, C22:C4, C4:C4, C2xC8, M4(2), C22xC4, C22xC4, C2xQ8, Dic5, C20, C20, C2xC10, C2xC10, C2xC10, Q8:C4, C42:C2, C2xM4(2), C22xQ8, C40, Dic10, Dic10, C2xDic5, C2xC20, C2xC20, C22xC10, C23.38D4, C4xDic5, C4:Dic5, C23.D5, C2xC40, C5xM4(2), C2xDic10, C2xDic10, C22xDic5, C22xC20, C20.44D4, C23.21D10, C10xM4(2), C22xDic10, C23.46D20
Quotients: C1, C2, C4, C22, C2xC4, D4, C23, D5, C22:C4, C22xC4, C2xD4, D10, C2xC22:C4, C8.C22, C4xD5, D20, C5:D4, C22xD5, C23.38D4, D10:C4, C2xC4xD5, C2xD20, C2xC5:D4, C8.D10, C2xD10:C4, C23.46D20
►On 160 points
Generators in S160
(1 102)(2 83)(3 104)(4 85)(5 106)(6 87)(7 108)(8 89)(9 110)(10 91)(11 112)(12 93)(13 114)(14 95)(15 116)(16 97)(17 118)(18 99)(19 120)(20 101)(21 82)(22 103)(23 84)(24 105)(25 86)(26 107)(27 88)(28 109)(29 90)(30 111)(31 92)(32 113)(33 94)(34 115)(35 96)(36 117)(37 98)(38 119)(39 100)(40 81)(41 140)(42 121)(43 142)(44 123)(45 144)(46 125)(47 146)(48 127)(49 148)(50 129)(51 150)(52 131)(53 152)(54 133)(55 154)(56 135)(57 156)(58 137)(59 158)(60 139)(61 160)(62 141)(63 122)(64 143)(65 124)(66 145)(67 126)(68 147)(69 128)(70 149)(71 130)(72 151)(73 132)(74 153)(75 134)(76 155)(77 136)(78 157)(79 138)(80 159)
(1 102)(2 103)(3 104)(4 105)(5 106)(6 107)(7 108)(8 109)(9 110)(10 111)(11 112)(12 113)(13 114)(14 115)(15 116)(16 117)(17 118)(18 119)(19 120)(20 81)(21 82)(22 83)(23 84)(24 85)(25 86)(26 87)(27 88)(28 89)(29 90)(30 91)(31 92)(32 93)(33 94)(34 95)(35 96)(36 97)(37 98)(38 99)(39 100)(40 101)(41 140)(42 141)(43 142)(44 143)(45 144)(46 145)(47 146)(48 147)(49 148)(50 149)(51 150)(52 151)(53 152)(54 153)(55 154)(56 155)(57 156)(58 157)(59 158)(60 159)(61 160)(62 121)(63 122)(64 123)(65 124)(66 125)(67 126)(68 127)(69 128)(70 129)(71 130)(72 131)(73 132)(74 133)(75 134)(76 135)(77 136)(78 137)(79 138)(80 139)
(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)
(1 134 21 154)(2 54 22 74)(3 132 23 152)(4 52 24 72)(5 130 25 150)(6 50 26 70)(7 128 27 148)(8 48 28 68)(9 126 29 146)(10 46 30 66)(11 124 31 144)(12 44 32 64)(13 122 33 142)(14 42 34 62)(15 160 35 140)(16 80 36 60)(17 158 37 138)(18 78 38 58)(19 156 39 136)(20 76 40 56)(41 116 61 96)(43 114 63 94)(45 112 65 92)(47 110 67 90)(49 108 69 88)(51 106 71 86)(53 104 73 84)(55 102 75 82)(57 100 77 120)(59 98 79 118)(81 135 101 155)(83 133 103 153)(85 131 105 151)(87 129 107 149)(89 127 109 147)(91 125 111 145)(93 123 113 143)(95 121 115 141)(97 159 117 139)(99 157 119 137)
G:=sub<Sym(160)| (1,102)(2,83)(3,104)(4,85)(5,106)(6,87)(7,108)(8,89)(9,110)(10,91)(11,112)(12,93)(13,114)(14,95)(15,116)(16,97)(17,118)(18,99)(19,120)(20,101)(21,82)(22,103)(23,84)(24,105)(25,86)(26,107)(27,88)(28,109)(29,90)(30,111)(31,92)(32,113)(33,94)(34,115)(35,96)(36,117)(37,98)(38,119)(39,100)(40,81)(41,140)(42,121)(43,142)(44,123)(45,144)(46,125)(47,146)(48,127)(49,148)(50,129)(51,150)(52,131)(53,152)(54,133)(55,154)(56,135)(57,156)(58,137)(59,158)(60,139)(61,160)(62,141)(63,122)(64,143)(65,124)(66,145)(67,126)(68,147)(69,128)(70,149)(71,130)(72,151)(73,132)(74,153)(75,134)(76,155)(77,136)(78,157)(79,138)(80,159), (1,102)(2,103)(3,104)(4,105)(5,106)(6,107)(7,108)(8,109)(9,110)(10,111)(11,112)(12,113)(13,114)(14,115)(15,116)(16,117)(17,118)(18,119)(19,120)(20,81)(21,82)(22,83)(23,84)(24,85)(25,86)(26,87)(27,88)(28,89)(29,90)(30,91)(31,92)(32,93)(33,94)(34,95)(35,96)(36,97)(37,98)(38,99)(39,100)(40,101)(41,140)(42,141)(43,142)(44,143)(45,144)(46,145)(47,146)(48,147)(49,148)(50,149)(51,150)(52,151)(53,152)(54,153)(55,154)(56,155)(57,156)(58,157)(59,158)(60,159)(61,160)(62,121)(63,122)(64,123)(65,124)(66,125)(67,126)(68,127)(69,128)(70,129)(71,130)(72,131)(73,132)(74,133)(75,134)(76,135)(77,136)(78,137)(79,138)(80,139), (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), (1,134,21,154)(2,54,22,74)(3,132,23,152)(4,52,24,72)(5,130,25,150)(6,50,26,70)(7,128,27,148)(8,48,28,68)(9,126,29,146)(10,46,30,66)(11,124,31,144)(12,44,32,64)(13,122,33,142)(14,42,34,62)(15,160,35,140)(16,80,36,60)(17,158,37,138)(18,78,38,58)(19,156,39,136)(20,76,40,56)(41,116,61,96)(43,114,63,94)(45,112,65,92)(47,110,67,90)(49,108,69,88)(51,106,71,86)(53,104,73,84)(55,102,75,82)(57,100,77,120)(59,98,79,118)(81,135,101,155)(83,133,103,153)(85,131,105,151)(87,129,107,149)(89,127,109,147)(91,125,111,145)(93,123,113,143)(95,121,115,141)(97,159,117,139)(99,157,119,137)>;
G:=Group( (1,102)(2,83)(3,104)(4,85)(5,106)(6,87)(7,108)(8,89)(9,110)(10,91)(11,112)(12,93)(13,114)(14,95)(15,116)(16,97)(17,118)(18,99)(19,120)(20,101)(21,82)(22,103)(23,84)(24,105)(25,86)(26,107)(27,88)(28,109)(29,90)(30,111)(31,92)(32,113)(33,94)(34,115)(35,96)(36,117)(37,98)(38,119)(39,100)(40,81)(41,140)(42,121)(43,142)(44,123)(45,144)(46,125)(47,146)(48,127)(49,148)(50,129)(51,150)(52,131)(53,152)(54,133)(55,154)(56,135)(57,156)(58,137)(59,158)(60,139)(61,160)(62,141)(63,122)(64,143)(65,124)(66,145)(67,126)(68,147)(69,128)(70,149)(71,130)(72,151)(73,132)(74,153)(75,134)(76,155)(77,136)(78,157)(79,138)(80,159), (1,102)(2,103)(3,104)(4,105)(5,106)(6,107)(7,108)(8,109)(9,110)(10,111)(11,112)(12,113)(13,114)(14,115)(15,116)(16,117)(17,118)(18,119)(19,120)(20,81)(21,82)(22,83)(23,84)(24,85)(25,86)(26,87)(27,88)(28,89)(29,90)(30,91)(31,92)(32,93)(33,94)(34,95)(35,96)(36,97)(37,98)(38,99)(39,100)(40,101)(41,140)(42,141)(43,142)(44,143)(45,144)(46,145)(47,146)(48,147)(49,148)(50,149)(51,150)(52,151)(53,152)(54,153)(55,154)(56,155)(57,156)(58,157)(59,158)(60,159)(61,160)(62,121)(63,122)(64,123)(65,124)(66,125)(67,126)(68,127)(69,128)(70,129)(71,130)(72,131)(73,132)(74,133)(75,134)(76,135)(77,136)(78,137)(79,138)(80,139), (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), (1,134,21,154)(2,54,22,74)(3,132,23,152)(4,52,24,72)(5,130,25,150)(6,50,26,70)(7,128,27,148)(8,48,28,68)(9,126,29,146)(10,46,30,66)(11,124,31,144)(12,44,32,64)(13,122,33,142)(14,42,34,62)(15,160,35,140)(16,80,36,60)(17,158,37,138)(18,78,38,58)(19,156,39,136)(20,76,40,56)(41,116,61,96)(43,114,63,94)(45,112,65,92)(47,110,67,90)(49,108,69,88)(51,106,71,86)(53,104,73,84)(55,102,75,82)(57,100,77,120)(59,98,79,118)(81,135,101,155)(83,133,103,153)(85,131,105,151)(87,129,107,149)(89,127,109,147)(91,125,111,145)(93,123,113,143)(95,121,115,141)(97,159,117,139)(99,157,119,137) );
G=PermutationGroup([[(1,102),(2,83),(3,104),(4,85),(5,106),(6,87),(7,108),(8,89),(9,110),(10,91),(11,112),(12,93),(13,114),(14,95),(15,116),(16,97),(17,118),(18,99),(19,120),(20,101),(21,82),(22,103),(23,84),(24,105),(25,86),(26,107),(27,88),(28,109),(29,90),(30,111),(31,92),(32,113),(33,94),(34,115),(35,96),(36,117),(37,98),(38,119),(39,100),(40,81),(41,140),(42,121),(43,142),(44,123),(45,144),(46,125),(47,146),(48,127),(49,148),(50,129),(51,150),(52,131),(53,152),(54,133),(55,154),(56,135),(57,156),(58,137),(59,158),(60,139),(61,160),(62,141),(63,122),(64,143),(65,124),(66,145),(67,126),(68,147),(69,128),(70,149),(71,130),(72,151),(73,132),(74,153),(75,134),(76,155),(77,136),(78,157),(79,138),(80,159)], [(1,102),(2,103),(3,104),(4,105),(5,106),(6,107),(7,108),(8,109),(9,110),(10,111),(11,112),(12,113),(13,114),(14,115),(15,116),(16,117),(17,118),(18,119),(19,120),(20,81),(21,82),(22,83),(23,84),(24,85),(25,86),(26,87),(27,88),(28,89),(29,90),(30,91),(31,92),(32,93),(33,94),(34,95),(35,96),(36,97),(37,98),(38,99),(39,100),(40,101),(41,140),(42,141),(43,142),(44,143),(45,144),(46,145),(47,146),(48,147),(49,148),(50,149),(51,150),(52,151),(53,152),(54,153),(55,154),(56,155),(57,156),(58,157),(59,158),(60,159),(61,160),(62,121),(63,122),(64,123),(65,124),(66,125),(67,126),(68,127),(69,128),(70,129),(71,130),(72,131),(73,132),(74,133),(75,134),(76,135),(77,136),(78,137),(79,138),(80,139)], [(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)], [(1,134,21,154),(2,54,22,74),(3,132,23,152),(4,52,24,72),(5,130,25,150),(6,50,26,70),(7,128,27,148),(8,48,28,68),(9,126,29,146),(10,46,30,66),(11,124,31,144),(12,44,32,64),(13,122,33,142),(14,42,34,62),(15,160,35,140),(16,80,36,60),(17,158,37,138),(18,78,38,58),(19,156,39,136),(20,76,40,56),(41,116,61,96),(43,114,63,94),(45,112,65,92),(47,110,67,90),(49,108,69,88),(51,106,71,86),(53,104,73,84),(55,102,75,82),(57,100,77,120),(59,98,79,118),(81,135,101,155),(83,133,103,153),(85,131,105,151),(87,129,107,149),(89,127,109,147),(91,125,111,145),(93,123,113,143),(95,121,115,141),(97,159,117,139),(99,157,119,137)]])
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 | C4xD5 | D20 | C5:D4 | D20 | C8.C22 | C8.D10 |
| kernel | C23.46D20 | C20.44D4 | C23.21D10 | C10xM4(2) | C22xDic10 | C2xDic10 | C2xC20 | C22xC10 | C2xM4(2) | C2xC8 | C22xC4 | C2xC4 | C2xC4 | C2xC4 | 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