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, C2, C4, C4, C22, C22, C5, C8, C2×C4, C2×C4, D4, C23, D5, C10, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, C2×D4, Dic5, C20, C20, D10, C2×C10, C22⋊C8, D4⋊C4, C4.Q8, C2.D8, C42⋊C2, C4⋊D4, C5⋊2C8, C40, C4×D5, D20, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×D5, C22×D5, C23.19D4, C2×C5⋊2C8, C4×Dic5, C4⋊Dic5, D10⋊C4, C5×C4⋊C4, 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, C22, D4, C23, D5, C2×D4, C4○D4, D10, 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)(9 117)(10 118)(11 119)(12 120)(13 113)(14 114)(15 115)(16 116)(17 92)(18 93)(19 94)(20 95)(21 96)(22 89)(23 90)(24 91)(25 124)(26 125)(27 126)(28 127)(29 128)(30 121)(31 122)(32 123)(33 75)(34 76)(35 77)(36 78)(37 79)(38 80)(39 73)(40 74)(41 101)(42 102)(43 103)(44 104)(45 97)(46 98)(47 99)(48 100)(49 141)(50 142)(51 143)(52 144)(53 137)(54 138)(55 139)(56 140)(57 85)(58 86)(59 87)(60 88)(61 81)(62 82)(63 83)(64 84)(105 130)(106 131)(107 132)(108 133)(109 134)(110 135)(111 136)(112 129)(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)(9 127 117 28)(10 126 118 27)(11 125 119 26)(12 124 120 25)(13 123 113 32)(14 122 114 31)(15 121 115 30)(16 128 116 29)(17 44 92 104)(18 43 93 103)(19 42 94 102)(20 41 95 101)(21 48 96 100)(22 47 89 99)(23 46 90 98)(24 45 91 97)(33 133 75 108)(34 132 76 107)(35 131 77 106)(36 130 78 105)(37 129 79 112)(38 136 80 111)(39 135 73 110)(40 134 74 109)(49 87 141 59)(50 86 142 58)(51 85 143 57)(52 84 144 64)(53 83 137 63)(54 82 138 62)(55 81 139 61)(56 88 140 60)
(1 61 17 37 26)(2 62 18 38 27)(3 63 19 39 28)(4 64 20 40 29)(5 57 21 33 30)(6 58 22 34 31)(7 59 23 35 32)(8 60 24 36 25)(9 150 53 42 135)(10 151 54 43 136)(11 152 55 44 129)(12 145 56 45 130)(13 146 49 46 131)(14 147 50 47 132)(15 148 51 48 133)(16 149 52 41 134)(65 82 93 80 126)(66 83 94 73 127)(67 84 95 74 128)(68 85 96 75 121)(69 86 89 76 122)(70 87 90 77 123)(71 88 91 78 124)(72 81 92 79 125)(97 105 120 157 140)(98 106 113 158 141)(99 107 114 159 142)(100 108 115 160 143)(101 109 116 153 144)(102 110 117 154 137)(103 111 118 155 138)(104 112 119 156 139)
(1 113)(2 10)(3 115)(4 12)(5 117)(6 14)(7 119)(8 16)(9 68)(11 70)(13 72)(15 66)(17 98)(18 43)(19 100)(20 45)(21 102)(22 47)(23 104)(24 41)(25 149)(26 158)(27 151)(28 160)(29 145)(30 154)(31 147)(32 156)(33 137)(34 50)(35 139)(36 52)(37 141)(38 54)(39 143)(40 56)(42 96)(44 90)(46 92)(48 94)(49 79)(51 73)(53 75)(55 77)(57 110)(58 132)(59 112)(60 134)(61 106)(62 136)(63 108)(64 130)(65 118)(67 120)(69 114)(71 116)(74 140)(76 142)(78 144)(80 138)(81 131)(82 111)(83 133)(84 105)(85 135)(86 107)(87 129)(88 109)(89 99)(91 101)(93 103)(95 97)(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)(9,117)(10,118)(11,119)(12,120)(13,113)(14,114)(15,115)(16,116)(17,92)(18,93)(19,94)(20,95)(21,96)(22,89)(23,90)(24,91)(25,124)(26,125)(27,126)(28,127)(29,128)(30,121)(31,122)(32,123)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,73)(40,74)(41,101)(42,102)(43,103)(44,104)(45,97)(46,98)(47,99)(48,100)(49,141)(50,142)(51,143)(52,144)(53,137)(54,138)(55,139)(56,140)(57,85)(58,86)(59,87)(60,88)(61,81)(62,82)(63,83)(64,84)(105,130)(106,131)(107,132)(108,133)(109,134)(110,135)(111,136)(112,129)(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)(9,127,117,28)(10,126,118,27)(11,125,119,26)(12,124,120,25)(13,123,113,32)(14,122,114,31)(15,121,115,30)(16,128,116,29)(17,44,92,104)(18,43,93,103)(19,42,94,102)(20,41,95,101)(21,48,96,100)(22,47,89,99)(23,46,90,98)(24,45,91,97)(33,133,75,108)(34,132,76,107)(35,131,77,106)(36,130,78,105)(37,129,79,112)(38,136,80,111)(39,135,73,110)(40,134,74,109)(49,87,141,59)(50,86,142,58)(51,85,143,57)(52,84,144,64)(53,83,137,63)(54,82,138,62)(55,81,139,61)(56,88,140,60), (1,61,17,37,26)(2,62,18,38,27)(3,63,19,39,28)(4,64,20,40,29)(5,57,21,33,30)(6,58,22,34,31)(7,59,23,35,32)(8,60,24,36,25)(9,150,53,42,135)(10,151,54,43,136)(11,152,55,44,129)(12,145,56,45,130)(13,146,49,46,131)(14,147,50,47,132)(15,148,51,48,133)(16,149,52,41,134)(65,82,93,80,126)(66,83,94,73,127)(67,84,95,74,128)(68,85,96,75,121)(69,86,89,76,122)(70,87,90,77,123)(71,88,91,78,124)(72,81,92,79,125)(97,105,120,157,140)(98,106,113,158,141)(99,107,114,159,142)(100,108,115,160,143)(101,109,116,153,144)(102,110,117,154,137)(103,111,118,155,138)(104,112,119,156,139), (1,113)(2,10)(3,115)(4,12)(5,117)(6,14)(7,119)(8,16)(9,68)(11,70)(13,72)(15,66)(17,98)(18,43)(19,100)(20,45)(21,102)(22,47)(23,104)(24,41)(25,149)(26,158)(27,151)(28,160)(29,145)(30,154)(31,147)(32,156)(33,137)(34,50)(35,139)(36,52)(37,141)(38,54)(39,143)(40,56)(42,96)(44,90)(46,92)(48,94)(49,79)(51,73)(53,75)(55,77)(57,110)(58,132)(59,112)(60,134)(61,106)(62,136)(63,108)(64,130)(65,118)(67,120)(69,114)(71,116)(74,140)(76,142)(78,144)(80,138)(81,131)(82,111)(83,133)(84,105)(85,135)(86,107)(87,129)(88,109)(89,99)(91,101)(93,103)(95,97)(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)(9,117)(10,118)(11,119)(12,120)(13,113)(14,114)(15,115)(16,116)(17,92)(18,93)(19,94)(20,95)(21,96)(22,89)(23,90)(24,91)(25,124)(26,125)(27,126)(28,127)(29,128)(30,121)(31,122)(32,123)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,73)(40,74)(41,101)(42,102)(43,103)(44,104)(45,97)(46,98)(47,99)(48,100)(49,141)(50,142)(51,143)(52,144)(53,137)(54,138)(55,139)(56,140)(57,85)(58,86)(59,87)(60,88)(61,81)(62,82)(63,83)(64,84)(105,130)(106,131)(107,132)(108,133)(109,134)(110,135)(111,136)(112,129)(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)(9,127,117,28)(10,126,118,27)(11,125,119,26)(12,124,120,25)(13,123,113,32)(14,122,114,31)(15,121,115,30)(16,128,116,29)(17,44,92,104)(18,43,93,103)(19,42,94,102)(20,41,95,101)(21,48,96,100)(22,47,89,99)(23,46,90,98)(24,45,91,97)(33,133,75,108)(34,132,76,107)(35,131,77,106)(36,130,78,105)(37,129,79,112)(38,136,80,111)(39,135,73,110)(40,134,74,109)(49,87,141,59)(50,86,142,58)(51,85,143,57)(52,84,144,64)(53,83,137,63)(54,82,138,62)(55,81,139,61)(56,88,140,60), (1,61,17,37,26)(2,62,18,38,27)(3,63,19,39,28)(4,64,20,40,29)(5,57,21,33,30)(6,58,22,34,31)(7,59,23,35,32)(8,60,24,36,25)(9,150,53,42,135)(10,151,54,43,136)(11,152,55,44,129)(12,145,56,45,130)(13,146,49,46,131)(14,147,50,47,132)(15,148,51,48,133)(16,149,52,41,134)(65,82,93,80,126)(66,83,94,73,127)(67,84,95,74,128)(68,85,96,75,121)(69,86,89,76,122)(70,87,90,77,123)(71,88,91,78,124)(72,81,92,79,125)(97,105,120,157,140)(98,106,113,158,141)(99,107,114,159,142)(100,108,115,160,143)(101,109,116,153,144)(102,110,117,154,137)(103,111,118,155,138)(104,112,119,156,139), (1,113)(2,10)(3,115)(4,12)(5,117)(6,14)(7,119)(8,16)(9,68)(11,70)(13,72)(15,66)(17,98)(18,43)(19,100)(20,45)(21,102)(22,47)(23,104)(24,41)(25,149)(26,158)(27,151)(28,160)(29,145)(30,154)(31,147)(32,156)(33,137)(34,50)(35,139)(36,52)(37,141)(38,54)(39,143)(40,56)(42,96)(44,90)(46,92)(48,94)(49,79)(51,73)(53,75)(55,77)(57,110)(58,132)(59,112)(60,134)(61,106)(62,136)(63,108)(64,130)(65,118)(67,120)(69,114)(71,116)(74,140)(76,142)(78,144)(80,138)(81,131)(82,111)(83,133)(84,105)(85,135)(86,107)(87,129)(88,109)(89,99)(91,101)(93,103)(95,97)(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),(9,117),(10,118),(11,119),(12,120),(13,113),(14,114),(15,115),(16,116),(17,92),(18,93),(19,94),(20,95),(21,96),(22,89),(23,90),(24,91),(25,124),(26,125),(27,126),(28,127),(29,128),(30,121),(31,122),(32,123),(33,75),(34,76),(35,77),(36,78),(37,79),(38,80),(39,73),(40,74),(41,101),(42,102),(43,103),(44,104),(45,97),(46,98),(47,99),(48,100),(49,141),(50,142),(51,143),(52,144),(53,137),(54,138),(55,139),(56,140),(57,85),(58,86),(59,87),(60,88),(61,81),(62,82),(63,83),(64,84),(105,130),(106,131),(107,132),(108,133),(109,134),(110,135),(111,136),(112,129),(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),(9,127,117,28),(10,126,118,27),(11,125,119,26),(12,124,120,25),(13,123,113,32),(14,122,114,31),(15,121,115,30),(16,128,116,29),(17,44,92,104),(18,43,93,103),(19,42,94,102),(20,41,95,101),(21,48,96,100),(22,47,89,99),(23,46,90,98),(24,45,91,97),(33,133,75,108),(34,132,76,107),(35,131,77,106),(36,130,78,105),(37,129,79,112),(38,136,80,111),(39,135,73,110),(40,134,74,109),(49,87,141,59),(50,86,142,58),(51,85,143,57),(52,84,144,64),(53,83,137,63),(54,82,138,62),(55,81,139,61),(56,88,140,60)], [(1,61,17,37,26),(2,62,18,38,27),(3,63,19,39,28),(4,64,20,40,29),(5,57,21,33,30),(6,58,22,34,31),(7,59,23,35,32),(8,60,24,36,25),(9,150,53,42,135),(10,151,54,43,136),(11,152,55,44,129),(12,145,56,45,130),(13,146,49,46,131),(14,147,50,47,132),(15,148,51,48,133),(16,149,52,41,134),(65,82,93,80,126),(66,83,94,73,127),(67,84,95,74,128),(68,85,96,75,121),(69,86,89,76,122),(70,87,90,77,123),(71,88,91,78,124),(72,81,92,79,125),(97,105,120,157,140),(98,106,113,158,141),(99,107,114,159,142),(100,108,115,160,143),(101,109,116,153,144),(102,110,117,154,137),(103,111,118,155,138),(104,112,119,156,139)], [(1,113),(2,10),(3,115),(4,12),(5,117),(6,14),(7,119),(8,16),(9,68),(11,70),(13,72),(15,66),(17,98),(18,43),(19,100),(20,45),(21,102),(22,47),(23,104),(24,41),(25,149),(26,158),(27,151),(28,160),(29,145),(30,154),(31,147),(32,156),(33,137),(34,50),(35,139),(36,52),(37,141),(38,54),(39,143),(40,56),(42,96),(44,90),(46,92),(48,94),(49,79),(51,73),(53,75),(55,77),(57,110),(58,132),(59,112),(60,134),(61,106),(62,136),(63,108),(64,130),(65,118),(67,120),(69,114),(71,116),(74,140),(76,142),(78,144),(80,138),(81,131),(82,111),(83,133),(84,105),(85,135),(86,107),(87,129),(88,109),(89,99),(91,101),(93,103),(95,97),(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