metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2.D8⋊5D5, C4⋊C4.50D10, (C2×C8).29D10, C4⋊D20.9C2, D20⋊5C4⋊27C2, D10⋊1C8⋊26C2, D20⋊6C4⋊22C2, C20.40(C4○D4), C4.82(C4○D20), C10.76(C4○D8), C20.Q8⋊21C2, (C22×D5).36D4, C22.231(D4×D5), C2.23(D8⋊D5), C10.42(C8⋊C22), (C2×C40).243C22, (C2×C20).301C23, C4.30(Q8⋊2D5), (C2×Dic5).224D4, (C2×D20).87C22, C5⋊5(C23.19D4), C2.14(Q8.D10), C4⋊Dic5.126C22, C2.17(D10.13D4), C10.47(C22.D4), C4⋊C4⋊7D5⋊7C2, (C5×C2.D8)⋊13C2, (C2×C4×D5).44C22, (C2×C10).306(C2×D4), (C5×C4⋊C4).94C22, (C2×C5⋊2C8).71C22, (C2×C4).404(C22×D5), SmallGroup(320,512)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2.D8⋊D5
G = < a,b,c,d,e | a2=b8=d5=e2=1, c2=a, ab=ba, ece=ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, ebe=ab5, cd=dc, ede=d-1 >
Subgroups: 526 in 106 conjugacy classes, 37 normal (all characteristic)
C1, C2 [×3], C2 [×2], C4 [×2], C4 [×4], C22, C22 [×6], C5, C8 [×2], C2×C4, C2×C4 [×6], D4 [×4], C23 [×2], D5 [×2], C10 [×3], C42, C22⋊C4 [×2], C4⋊C4 [×2], C4⋊C4, C2×C8, C2×C8, C22×C4, C2×D4 [×2], Dic5 [×2], C20 [×2], C20 [×2], D10 [×6], C2×C10, C22⋊C8, D4⋊C4 [×2], C4.Q8, C2.D8, C42⋊C2, C4⋊D4, C5⋊2C8, C40, C4×D5 [×2], D20 [×4], C2×Dic5, C2×Dic5, C2×C20, C2×C20 [×2], C22×D5, C22×D5, C23.19D4, C2×C5⋊2C8, C4×Dic5, C4⋊Dic5, D10⋊C4 [×2], C5×C4⋊C4 [×2], C2×C40, C2×C4×D5, C2×D20, C2×D20, C20.Q8, D20⋊6C4, D10⋊1C8, D20⋊5C4, C5×C2.D8, C4⋊C4⋊7D5, C4⋊D20, C2.D8⋊D5
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, D5, C2×D4, C4○D4 [×2], D10 [×3], C22.D4, C4○D8, C8⋊C22, C22×D5, C23.19D4, C4○D20, D4×D5, Q8⋊2D5, D10.13D4, D8⋊D5, Q8.D10, C2.D8⋊D5
►On 160 points
Generators in S160
(1 72)(2 65)(3 66)(4 67)(5 68)(6 69)(7 70)(8 71)(9 138)(10 139)(11 140)(12 141)(13 142)(14 143)(15 144)(16 137)(17 90)(18 91)(19 92)(20 93)(21 94)(22 95)(23 96)(24 89)(25 36)(26 37)(27 38)(28 39)(29 40)(30 33)(31 34)(32 35)(41 118)(42 119)(43 120)(44 113)(45 114)(46 115)(47 116)(48 117)(49 98)(50 99)(51 100)(52 101)(53 102)(54 103)(55 104)(56 97)(57 85)(58 86)(59 87)(60 88)(61 81)(62 82)(63 83)(64 84)(73 123)(74 124)(75 125)(76 126)(77 127)(78 128)(79 121)(80 122)(105 135)(106 136)(107 129)(108 130)(109 131)(110 132)(111 133)(112 134)(145 157)(146 158)(147 159)(148 160)(149 153)(150 154)(151 155)(152 156)
(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)
(1 152 72 156)(2 151 65 155)(3 150 66 154)(4 149 67 153)(5 148 68 160)(6 147 69 159)(7 146 70 158)(8 145 71 157)(9 127 138 77)(10 126 139 76)(11 125 140 75)(12 124 141 74)(13 123 142 73)(14 122 143 80)(15 121 144 79)(16 128 137 78)(17 46 90 115)(18 45 91 114)(19 44 92 113)(20 43 93 120)(21 42 94 119)(22 41 95 118)(23 48 96 117)(24 47 89 116)(25 105 36 135)(26 112 37 134)(27 111 38 133)(28 110 39 132)(29 109 40 131)(30 108 33 130)(31 107 34 129)(32 106 35 136)(49 87 98 59)(50 86 99 58)(51 85 100 57)(52 84 101 64)(53 83 102 63)(54 82 103 62)(55 81 104 61)(56 88 97 60)
(1 61 19 37 75)(2 62 20 38 76)(3 63 21 39 77)(4 64 22 40 78)(5 57 23 33 79)(6 58 24 34 80)(7 59 17 35 73)(8 60 18 36 74)(9 150 53 42 132)(10 151 54 43 133)(11 152 55 44 134)(12 145 56 45 135)(13 146 49 46 136)(14 147 50 47 129)(15 148 51 48 130)(16 149 52 41 131)(25 124 71 88 91)(26 125 72 81 92)(27 126 65 82 93)(28 127 66 83 94)(29 128 67 84 95)(30 121 68 85 96)(31 122 69 86 89)(32 123 70 87 90)(97 114 105 141 157)(98 115 106 142 158)(99 116 107 143 159)(100 117 108 144 160)(101 118 109 137 153)(102 119 110 138 154)(103 120 111 139 155)(104 113 112 140 156)
(1 142)(2 10)(3 144)(4 12)(5 138)(6 14)(7 140)(8 16)(9 68)(11 70)(13 72)(15 66)(17 113)(18 41)(19 115)(20 43)(21 117)(22 45)(23 119)(24 47)(25 101)(26 49)(27 103)(28 51)(29 97)(30 53)(31 99)(32 55)(33 102)(34 50)(35 104)(36 52)(37 98)(38 54)(39 100)(40 56)(42 96)(44 90)(46 92)(48 94)(57 110)(58 129)(59 112)(60 131)(61 106)(62 133)(63 108)(64 135)(65 139)(67 141)(69 143)(71 137)(73 156)(74 149)(75 158)(76 151)(77 160)(78 145)(79 154)(80 147)(81 136)(82 111)(83 130)(84 105)(85 132)(86 107)(87 134)(88 109)(89 116)(91 118)(93 120)(95 114)(121 150)(122 159)(123 152)(124 153)(125 146)(126 155)(127 148)(128 157)
G:=sub<Sym(160)| (1,72)(2,65)(3,66)(4,67)(5,68)(6,69)(7,70)(8,71)(9,138)(10,139)(11,140)(12,141)(13,142)(14,143)(15,144)(16,137)(17,90)(18,91)(19,92)(20,93)(21,94)(22,95)(23,96)(24,89)(25,36)(26,37)(27,38)(28,39)(29,40)(30,33)(31,34)(32,35)(41,118)(42,119)(43,120)(44,113)(45,114)(46,115)(47,116)(48,117)(49,98)(50,99)(51,100)(52,101)(53,102)(54,103)(55,104)(56,97)(57,85)(58,86)(59,87)(60,88)(61,81)(62,82)(63,83)(64,84)(73,123)(74,124)(75,125)(76,126)(77,127)(78,128)(79,121)(80,122)(105,135)(106,136)(107,129)(108,130)(109,131)(110,132)(111,133)(112,134)(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)(152,156), (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), (1,152,72,156)(2,151,65,155)(3,150,66,154)(4,149,67,153)(5,148,68,160)(6,147,69,159)(7,146,70,158)(8,145,71,157)(9,127,138,77)(10,126,139,76)(11,125,140,75)(12,124,141,74)(13,123,142,73)(14,122,143,80)(15,121,144,79)(16,128,137,78)(17,46,90,115)(18,45,91,114)(19,44,92,113)(20,43,93,120)(21,42,94,119)(22,41,95,118)(23,48,96,117)(24,47,89,116)(25,105,36,135)(26,112,37,134)(27,111,38,133)(28,110,39,132)(29,109,40,131)(30,108,33,130)(31,107,34,129)(32,106,35,136)(49,87,98,59)(50,86,99,58)(51,85,100,57)(52,84,101,64)(53,83,102,63)(54,82,103,62)(55,81,104,61)(56,88,97,60), (1,61,19,37,75)(2,62,20,38,76)(3,63,21,39,77)(4,64,22,40,78)(5,57,23,33,79)(6,58,24,34,80)(7,59,17,35,73)(8,60,18,36,74)(9,150,53,42,132)(10,151,54,43,133)(11,152,55,44,134)(12,145,56,45,135)(13,146,49,46,136)(14,147,50,47,129)(15,148,51,48,130)(16,149,52,41,131)(25,124,71,88,91)(26,125,72,81,92)(27,126,65,82,93)(28,127,66,83,94)(29,128,67,84,95)(30,121,68,85,96)(31,122,69,86,89)(32,123,70,87,90)(97,114,105,141,157)(98,115,106,142,158)(99,116,107,143,159)(100,117,108,144,160)(101,118,109,137,153)(102,119,110,138,154)(103,120,111,139,155)(104,113,112,140,156), (1,142)(2,10)(3,144)(4,12)(5,138)(6,14)(7,140)(8,16)(9,68)(11,70)(13,72)(15,66)(17,113)(18,41)(19,115)(20,43)(21,117)(22,45)(23,119)(24,47)(25,101)(26,49)(27,103)(28,51)(29,97)(30,53)(31,99)(32,55)(33,102)(34,50)(35,104)(36,52)(37,98)(38,54)(39,100)(40,56)(42,96)(44,90)(46,92)(48,94)(57,110)(58,129)(59,112)(60,131)(61,106)(62,133)(63,108)(64,135)(65,139)(67,141)(69,143)(71,137)(73,156)(74,149)(75,158)(76,151)(77,160)(78,145)(79,154)(80,147)(81,136)(82,111)(83,130)(84,105)(85,132)(86,107)(87,134)(88,109)(89,116)(91,118)(93,120)(95,114)(121,150)(122,159)(123,152)(124,153)(125,146)(126,155)(127,148)(128,157)>;
G:=Group( (1,72)(2,65)(3,66)(4,67)(5,68)(6,69)(7,70)(8,71)(9,138)(10,139)(11,140)(12,141)(13,142)(14,143)(15,144)(16,137)(17,90)(18,91)(19,92)(20,93)(21,94)(22,95)(23,96)(24,89)(25,36)(26,37)(27,38)(28,39)(29,40)(30,33)(31,34)(32,35)(41,118)(42,119)(43,120)(44,113)(45,114)(46,115)(47,116)(48,117)(49,98)(50,99)(51,100)(52,101)(53,102)(54,103)(55,104)(56,97)(57,85)(58,86)(59,87)(60,88)(61,81)(62,82)(63,83)(64,84)(73,123)(74,124)(75,125)(76,126)(77,127)(78,128)(79,121)(80,122)(105,135)(106,136)(107,129)(108,130)(109,131)(110,132)(111,133)(112,134)(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)(152,156), (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), (1,152,72,156)(2,151,65,155)(3,150,66,154)(4,149,67,153)(5,148,68,160)(6,147,69,159)(7,146,70,158)(8,145,71,157)(9,127,138,77)(10,126,139,76)(11,125,140,75)(12,124,141,74)(13,123,142,73)(14,122,143,80)(15,121,144,79)(16,128,137,78)(17,46,90,115)(18,45,91,114)(19,44,92,113)(20,43,93,120)(21,42,94,119)(22,41,95,118)(23,48,96,117)(24,47,89,116)(25,105,36,135)(26,112,37,134)(27,111,38,133)(28,110,39,132)(29,109,40,131)(30,108,33,130)(31,107,34,129)(32,106,35,136)(49,87,98,59)(50,86,99,58)(51,85,100,57)(52,84,101,64)(53,83,102,63)(54,82,103,62)(55,81,104,61)(56,88,97,60), (1,61,19,37,75)(2,62,20,38,76)(3,63,21,39,77)(4,64,22,40,78)(5,57,23,33,79)(6,58,24,34,80)(7,59,17,35,73)(8,60,18,36,74)(9,150,53,42,132)(10,151,54,43,133)(11,152,55,44,134)(12,145,56,45,135)(13,146,49,46,136)(14,147,50,47,129)(15,148,51,48,130)(16,149,52,41,131)(25,124,71,88,91)(26,125,72,81,92)(27,126,65,82,93)(28,127,66,83,94)(29,128,67,84,95)(30,121,68,85,96)(31,122,69,86,89)(32,123,70,87,90)(97,114,105,141,157)(98,115,106,142,158)(99,116,107,143,159)(100,117,108,144,160)(101,118,109,137,153)(102,119,110,138,154)(103,120,111,139,155)(104,113,112,140,156), (1,142)(2,10)(3,144)(4,12)(5,138)(6,14)(7,140)(8,16)(9,68)(11,70)(13,72)(15,66)(17,113)(18,41)(19,115)(20,43)(21,117)(22,45)(23,119)(24,47)(25,101)(26,49)(27,103)(28,51)(29,97)(30,53)(31,99)(32,55)(33,102)(34,50)(35,104)(36,52)(37,98)(38,54)(39,100)(40,56)(42,96)(44,90)(46,92)(48,94)(57,110)(58,129)(59,112)(60,131)(61,106)(62,133)(63,108)(64,135)(65,139)(67,141)(69,143)(71,137)(73,156)(74,149)(75,158)(76,151)(77,160)(78,145)(79,154)(80,147)(81,136)(82,111)(83,130)(84,105)(85,132)(86,107)(87,134)(88,109)(89,116)(91,118)(93,120)(95,114)(121,150)(122,159)(123,152)(124,153)(125,146)(126,155)(127,148)(128,157) );
G=PermutationGroup([(1,72),(2,65),(3,66),(4,67),(5,68),(6,69),(7,70),(8,71),(9,138),(10,139),(11,140),(12,141),(13,142),(14,143),(15,144),(16,137),(17,90),(18,91),(19,92),(20,93),(21,94),(22,95),(23,96),(24,89),(25,36),(26,37),(27,38),(28,39),(29,40),(30,33),(31,34),(32,35),(41,118),(42,119),(43,120),(44,113),(45,114),(46,115),(47,116),(48,117),(49,98),(50,99),(51,100),(52,101),(53,102),(54,103),(55,104),(56,97),(57,85),(58,86),(59,87),(60,88),(61,81),(62,82),(63,83),(64,84),(73,123),(74,124),(75,125),(76,126),(77,127),(78,128),(79,121),(80,122),(105,135),(106,136),(107,129),(108,130),(109,131),(110,132),(111,133),(112,134),(145,157),(146,158),(147,159),(148,160),(149,153),(150,154),(151,155),(152,156)], [(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)], [(1,152,72,156),(2,151,65,155),(3,150,66,154),(4,149,67,153),(5,148,68,160),(6,147,69,159),(7,146,70,158),(8,145,71,157),(9,127,138,77),(10,126,139,76),(11,125,140,75),(12,124,141,74),(13,123,142,73),(14,122,143,80),(15,121,144,79),(16,128,137,78),(17,46,90,115),(18,45,91,114),(19,44,92,113),(20,43,93,120),(21,42,94,119),(22,41,95,118),(23,48,96,117),(24,47,89,116),(25,105,36,135),(26,112,37,134),(27,111,38,133),(28,110,39,132),(29,109,40,131),(30,108,33,130),(31,107,34,129),(32,106,35,136),(49,87,98,59),(50,86,99,58),(51,85,100,57),(52,84,101,64),(53,83,102,63),(54,82,103,62),(55,81,104,61),(56,88,97,60)], [(1,61,19,37,75),(2,62,20,38,76),(3,63,21,39,77),(4,64,22,40,78),(5,57,23,33,79),(6,58,24,34,80),(7,59,17,35,73),(8,60,18,36,74),(9,150,53,42,132),(10,151,54,43,133),(11,152,55,44,134),(12,145,56,45,135),(13,146,49,46,136),(14,147,50,47,129),(15,148,51,48,130),(16,149,52,41,131),(25,124,71,88,91),(26,125,72,81,92),(27,126,65,82,93),(28,127,66,83,94),(29,128,67,84,95),(30,121,68,85,96),(31,122,69,86,89),(32,123,70,87,90),(97,114,105,141,157),(98,115,106,142,158),(99,116,107,143,159),(100,117,108,144,160),(101,118,109,137,153),(102,119,110,138,154),(103,120,111,139,155),(104,113,112,140,156)], [(1,142),(2,10),(3,144),(4,12),(5,138),(6,14),(7,140),(8,16),(9,68),(11,70),(13,72),(15,66),(17,113),(18,41),(19,115),(20,43),(21,117),(22,45),(23,119),(24,47),(25,101),(26,49),(27,103),(28,51),(29,97),(30,53),(31,99),(32,55),(33,102),(34,50),(35,104),(36,52),(37,98),(38,54),(39,100),(40,56),(42,96),(44,90),(46,92),(48,94),(57,110),(58,129),(59,112),(60,131),(61,106),(62,133),(63,108),(64,135),(65,139),(67,141),(69,143),(71,137),(73,156),(74,149),(75,158),(76,151),(77,160),(78,145),(79,154),(80,147),(81,136),(82,111),(83,130),(84,105),(85,132),(86,107),(87,134),(88,109),(89,116),(91,118),(93,120),(95,114),(121,150),(122,159),(123,152),(124,153),(125,146),(126,155),(127,148),(128,157)])
47 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 5A | 5B | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 20A | 20B | 20C | 20D | 20E | ··· | 20L | 40A | ··· | 40H |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 20 | 40 | 2 | 2 | 4 | 4 | 8 | 10 | 10 | 20 | 20 | 2 | 2 | 4 | 4 | 20 | 20 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
47 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D5 | C4○D4 | D10 | D10 | C4○D8 | C4○D20 | C8⋊C22 | Q8⋊2D5 | D4×D5 | D8⋊D5 | Q8.D10 |
| kernel | C2.D8⋊D5 | C20.Q8 | D20⋊6C4 | D10⋊1C8 | D20⋊5C4 | C5×C2.D8 | C4⋊C4⋊7D5 | C4⋊D20 | C2×Dic5 | C22×D5 | C2.D8 | C20 | C4⋊C4 | C2×C8 | C10 | C4 | C10 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 4 | 4 | 2 | 4 | 8 | 1 | 2 | 2 | 4 | 4 |
Matrix representation of C2.D8⋊D5 ►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 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 33 | 0 | 0 |
| 0 | 0 | 3 | 36 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 29 |
| 0 | 0 | 0 | 0 | 12 | 12 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 37 | 31 | 0 | 0 |
| 0 | 0 | 14 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 0 | 0 | 32 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 40 | 34 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 37 | 31 | 0 | 0 |
| 0 | 0 | 22 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 9 |
| 0 | 0 | 0 | 0 | 32 | 0 |
G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,5,3,0,0,0,0,33,36,0,0,0,0,0,0,12,12,0,0,0,0,29,12],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,37,14,0,0,0,0,31,4,0,0,0,0,0,0,9,0,0,0,0,0,0,32],[0,40,0,0,0,0,1,34,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,40,0,0,0,0,40,0,0,0,0,0,0,0,37,22,0,0,0,0,31,4,0,0,0,0,0,0,0,32,0,0,0,0,9,0] >;
C2.D8⋊D5 in GAP, Magma, Sage, TeX
C_2.D_8\rtimes D_5
% in TeX
G:=Group("C2.D8:D5"); // GroupNames label
G:=SmallGroup(320,512);
// by ID
G=gap.SmallGroup(320,512);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,477,64,926,219,268,851,102,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^8=d^5=e^2=1,c^2=a,a*b=b*a,e*c*e=a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=b^-1,b*d=d*b,e*b*e=a*b^5,c*d=d*c,e*d*e=d^-1>;
// generators/relations