direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D10.13D4, C4⋊C4⋊37D10, D10.71(C2×D4), (C2×C10).49C24, (C22×D20).9C2, C10.42(C22×D4), C22.132(D4×D5), (C2×C20).616C23, (C22×D5).132D4, (C22×C4).318D10, D10⋊C4⋊64C22, C22.83(C23×D5), (C2×D20).213C22, C22.76(C4○D20), C10.D4⋊51C22, C10⋊3(C22.D4), (C22×D5).12C23, C23.327(C22×D5), (C22×C10).398C23, (C22×C20).359C22, C22.35(Q8⋊2D5), (C2×Dic5).197C23, (C23×D5).111C22, (C22×Dic5).235C22, C2.14(C2×D4×D5), (C2×C4⋊C4)⋊14D5, (C10×C4⋊C4)⋊11C2, (D5×C22×C4)⋊20C2, (C2×C4×D5)⋊68C22, (C5×C4⋊C4)⋊45C22, C2.21(C2×C4○D20), C10.19(C2×C4○D4), C2.6(C2×Q8⋊2D5), C5⋊3(C2×C22.D4), (C2×C10).388(C2×D4), (C2×D10⋊C4)⋊33C2, (C2×C10.D4)⋊23C2, (C2×C4).140(C22×D5), (C2×C10).106(C4○D4), SmallGroup(320,1177)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D10.13D4
G = < a,b,c,d,e | a2=b10=c2=d4=1, e2=b5, ab=ba, ac=ca, ad=da, ae=ea, cbc=b-1, bd=db, be=eb, dcd-1=ece-1=b5c, ede-1=d-1 >
Subgroups: 1374 in 342 conjugacy classes, 119 normal (31 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, C23, C23, D5, C10, C10, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C24, Dic5, C20, D10, D10, C2×C10, C2×C10, C2×C22⋊C4, C2×C4⋊C4, C2×C4⋊C4, C22.D4, C23×C4, C22×D4, C4×D5, D20, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×D5, C22×D5, C22×C10, C2×C22.D4, C10.D4, D10⋊C4, C5×C4⋊C4, C2×C4×D5, C2×C4×D5, C2×D20, C2×D20, C22×Dic5, C22×C20, C23×D5, D10.13D4, C2×C10.D4, C2×D10⋊C4, C10×C4⋊C4, D5×C22×C4, C22×D20, C2×D10.13D4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C4○D4, C24, D10, C22.D4, C22×D4, C2×C4○D4, C22×D5, C2×C22.D4, C4○D20, D4×D5, Q8⋊2D5, C23×D5, D10.13D4, C2×C4○D20, C2×D4×D5, C2×Q8⋊2D5, C2×D10.13D4
►On 160 points
Generators in S160
(1 105)(2 106)(3 107)(4 108)(5 109)(6 110)(7 101)(8 102)(9 103)(10 104)(11 78)(12 79)(13 80)(14 71)(15 72)(16 73)(17 74)(18 75)(19 76)(20 77)(21 94)(22 95)(23 96)(24 97)(25 98)(26 99)(27 100)(28 91)(29 92)(30 93)(31 128)(32 129)(33 130)(34 121)(35 122)(36 123)(37 124)(38 125)(39 126)(40 127)(41 114)(42 115)(43 116)(44 117)(45 118)(46 119)(47 120)(48 111)(49 112)(50 113)(51 148)(52 149)(53 150)(54 141)(55 142)(56 143)(57 144)(58 145)(59 146)(60 147)(61 134)(62 135)(63 136)(64 137)(65 138)(66 139)(67 140)(68 131)(69 132)(70 133)(81 154)(82 155)(83 156)(84 157)(85 158)(86 159)(87 160)(88 151)(89 152)(90 153)
(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 84)(2 83)(3 82)(4 81)(5 90)(6 89)(7 88)(8 87)(9 86)(10 85)(11 97)(12 96)(13 95)(14 94)(15 93)(16 92)(17 91)(18 100)(19 99)(20 98)(21 71)(22 80)(23 79)(24 78)(25 77)(26 76)(27 75)(28 74)(29 73)(30 72)(31 66)(32 65)(33 64)(34 63)(35 62)(36 61)(37 70)(38 69)(39 68)(40 67)(41 56)(42 55)(43 54)(44 53)(45 52)(46 51)(47 60)(48 59)(49 58)(50 57)(101 151)(102 160)(103 159)(104 158)(105 157)(106 156)(107 155)(108 154)(109 153)(110 152)(111 146)(112 145)(113 144)(114 143)(115 142)(116 141)(117 150)(118 149)(119 148)(120 147)(121 136)(122 135)(123 134)(124 133)(125 132)(126 131)(127 140)(128 139)(129 138)(130 137)
(1 125 25 118)(2 126 26 119)(3 127 27 120)(4 128 28 111)(5 129 29 112)(6 130 30 113)(7 121 21 114)(8 122 22 115)(9 123 23 116)(10 124 24 117)(11 58 158 65)(12 59 159 66)(13 60 160 67)(14 51 151 68)(15 52 152 69)(16 53 153 70)(17 54 154 61)(18 55 155 62)(19 56 156 63)(20 57 157 64)(31 91 48 108)(32 92 49 109)(33 93 50 110)(34 94 41 101)(35 95 42 102)(36 96 43 103)(37 97 44 104)(38 98 45 105)(39 99 46 106)(40 100 47 107)(71 148 88 131)(72 149 89 132)(73 150 90 133)(74 141 81 134)(75 142 82 135)(76 143 83 136)(77 144 84 137)(78 145 85 138)(79 146 86 139)(80 147 87 140)
(1 16 6 11)(2 17 7 12)(3 18 8 13)(4 19 9 14)(5 20 10 15)(21 159 26 154)(22 160 27 155)(23 151 28 156)(24 152 29 157)(25 153 30 158)(31 136 36 131)(32 137 37 132)(33 138 38 133)(34 139 39 134)(35 140 40 135)(41 146 46 141)(42 147 47 142)(43 148 48 143)(44 149 49 144)(45 150 50 145)(51 111 56 116)(52 112 57 117)(53 113 58 118)(54 114 59 119)(55 115 60 120)(61 121 66 126)(62 122 67 127)(63 123 68 128)(64 124 69 129)(65 125 70 130)(71 108 76 103)(72 109 77 104)(73 110 78 105)(74 101 79 106)(75 102 80 107)(81 94 86 99)(82 95 87 100)(83 96 88 91)(84 97 89 92)(85 98 90 93)
G:=sub<Sym(160)| (1,105)(2,106)(3,107)(4,108)(5,109)(6,110)(7,101)(8,102)(9,103)(10,104)(11,78)(12,79)(13,80)(14,71)(15,72)(16,73)(17,74)(18,75)(19,76)(20,77)(21,94)(22,95)(23,96)(24,97)(25,98)(26,99)(27,100)(28,91)(29,92)(30,93)(31,128)(32,129)(33,130)(34,121)(35,122)(36,123)(37,124)(38,125)(39,126)(40,127)(41,114)(42,115)(43,116)(44,117)(45,118)(46,119)(47,120)(48,111)(49,112)(50,113)(51,148)(52,149)(53,150)(54,141)(55,142)(56,143)(57,144)(58,145)(59,146)(60,147)(61,134)(62,135)(63,136)(64,137)(65,138)(66,139)(67,140)(68,131)(69,132)(70,133)(81,154)(82,155)(83,156)(84,157)(85,158)(86,159)(87,160)(88,151)(89,152)(90,153), (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), (1,84)(2,83)(3,82)(4,81)(5,90)(6,89)(7,88)(8,87)(9,86)(10,85)(11,97)(12,96)(13,95)(14,94)(15,93)(16,92)(17,91)(18,100)(19,99)(20,98)(21,71)(22,80)(23,79)(24,78)(25,77)(26,76)(27,75)(28,74)(29,73)(30,72)(31,66)(32,65)(33,64)(34,63)(35,62)(36,61)(37,70)(38,69)(39,68)(40,67)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,60)(48,59)(49,58)(50,57)(101,151)(102,160)(103,159)(104,158)(105,157)(106,156)(107,155)(108,154)(109,153)(110,152)(111,146)(112,145)(113,144)(114,143)(115,142)(116,141)(117,150)(118,149)(119,148)(120,147)(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,140)(128,139)(129,138)(130,137), (1,125,25,118)(2,126,26,119)(3,127,27,120)(4,128,28,111)(5,129,29,112)(6,130,30,113)(7,121,21,114)(8,122,22,115)(9,123,23,116)(10,124,24,117)(11,58,158,65)(12,59,159,66)(13,60,160,67)(14,51,151,68)(15,52,152,69)(16,53,153,70)(17,54,154,61)(18,55,155,62)(19,56,156,63)(20,57,157,64)(31,91,48,108)(32,92,49,109)(33,93,50,110)(34,94,41,101)(35,95,42,102)(36,96,43,103)(37,97,44,104)(38,98,45,105)(39,99,46,106)(40,100,47,107)(71,148,88,131)(72,149,89,132)(73,150,90,133)(74,141,81,134)(75,142,82,135)(76,143,83,136)(77,144,84,137)(78,145,85,138)(79,146,86,139)(80,147,87,140), (1,16,6,11)(2,17,7,12)(3,18,8,13)(4,19,9,14)(5,20,10,15)(21,159,26,154)(22,160,27,155)(23,151,28,156)(24,152,29,157)(25,153,30,158)(31,136,36,131)(32,137,37,132)(33,138,38,133)(34,139,39,134)(35,140,40,135)(41,146,46,141)(42,147,47,142)(43,148,48,143)(44,149,49,144)(45,150,50,145)(51,111,56,116)(52,112,57,117)(53,113,58,118)(54,114,59,119)(55,115,60,120)(61,121,66,126)(62,122,67,127)(63,123,68,128)(64,124,69,129)(65,125,70,130)(71,108,76,103)(72,109,77,104)(73,110,78,105)(74,101,79,106)(75,102,80,107)(81,94,86,99)(82,95,87,100)(83,96,88,91)(84,97,89,92)(85,98,90,93)>;
G:=Group( (1,105)(2,106)(3,107)(4,108)(5,109)(6,110)(7,101)(8,102)(9,103)(10,104)(11,78)(12,79)(13,80)(14,71)(15,72)(16,73)(17,74)(18,75)(19,76)(20,77)(21,94)(22,95)(23,96)(24,97)(25,98)(26,99)(27,100)(28,91)(29,92)(30,93)(31,128)(32,129)(33,130)(34,121)(35,122)(36,123)(37,124)(38,125)(39,126)(40,127)(41,114)(42,115)(43,116)(44,117)(45,118)(46,119)(47,120)(48,111)(49,112)(50,113)(51,148)(52,149)(53,150)(54,141)(55,142)(56,143)(57,144)(58,145)(59,146)(60,147)(61,134)(62,135)(63,136)(64,137)(65,138)(66,139)(67,140)(68,131)(69,132)(70,133)(81,154)(82,155)(83,156)(84,157)(85,158)(86,159)(87,160)(88,151)(89,152)(90,153), (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), (1,84)(2,83)(3,82)(4,81)(5,90)(6,89)(7,88)(8,87)(9,86)(10,85)(11,97)(12,96)(13,95)(14,94)(15,93)(16,92)(17,91)(18,100)(19,99)(20,98)(21,71)(22,80)(23,79)(24,78)(25,77)(26,76)(27,75)(28,74)(29,73)(30,72)(31,66)(32,65)(33,64)(34,63)(35,62)(36,61)(37,70)(38,69)(39,68)(40,67)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,60)(48,59)(49,58)(50,57)(101,151)(102,160)(103,159)(104,158)(105,157)(106,156)(107,155)(108,154)(109,153)(110,152)(111,146)(112,145)(113,144)(114,143)(115,142)(116,141)(117,150)(118,149)(119,148)(120,147)(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,140)(128,139)(129,138)(130,137), (1,125,25,118)(2,126,26,119)(3,127,27,120)(4,128,28,111)(5,129,29,112)(6,130,30,113)(7,121,21,114)(8,122,22,115)(9,123,23,116)(10,124,24,117)(11,58,158,65)(12,59,159,66)(13,60,160,67)(14,51,151,68)(15,52,152,69)(16,53,153,70)(17,54,154,61)(18,55,155,62)(19,56,156,63)(20,57,157,64)(31,91,48,108)(32,92,49,109)(33,93,50,110)(34,94,41,101)(35,95,42,102)(36,96,43,103)(37,97,44,104)(38,98,45,105)(39,99,46,106)(40,100,47,107)(71,148,88,131)(72,149,89,132)(73,150,90,133)(74,141,81,134)(75,142,82,135)(76,143,83,136)(77,144,84,137)(78,145,85,138)(79,146,86,139)(80,147,87,140), (1,16,6,11)(2,17,7,12)(3,18,8,13)(4,19,9,14)(5,20,10,15)(21,159,26,154)(22,160,27,155)(23,151,28,156)(24,152,29,157)(25,153,30,158)(31,136,36,131)(32,137,37,132)(33,138,38,133)(34,139,39,134)(35,140,40,135)(41,146,46,141)(42,147,47,142)(43,148,48,143)(44,149,49,144)(45,150,50,145)(51,111,56,116)(52,112,57,117)(53,113,58,118)(54,114,59,119)(55,115,60,120)(61,121,66,126)(62,122,67,127)(63,123,68,128)(64,124,69,129)(65,125,70,130)(71,108,76,103)(72,109,77,104)(73,110,78,105)(74,101,79,106)(75,102,80,107)(81,94,86,99)(82,95,87,100)(83,96,88,91)(84,97,89,92)(85,98,90,93) );
G=PermutationGroup([[(1,105),(2,106),(3,107),(4,108),(5,109),(6,110),(7,101),(8,102),(9,103),(10,104),(11,78),(12,79),(13,80),(14,71),(15,72),(16,73),(17,74),(18,75),(19,76),(20,77),(21,94),(22,95),(23,96),(24,97),(25,98),(26,99),(27,100),(28,91),(29,92),(30,93),(31,128),(32,129),(33,130),(34,121),(35,122),(36,123),(37,124),(38,125),(39,126),(40,127),(41,114),(42,115),(43,116),(44,117),(45,118),(46,119),(47,120),(48,111),(49,112),(50,113),(51,148),(52,149),(53,150),(54,141),(55,142),(56,143),(57,144),(58,145),(59,146),(60,147),(61,134),(62,135),(63,136),(64,137),(65,138),(66,139),(67,140),(68,131),(69,132),(70,133),(81,154),(82,155),(83,156),(84,157),(85,158),(86,159),(87,160),(88,151),(89,152),(90,153)], [(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)], [(1,84),(2,83),(3,82),(4,81),(5,90),(6,89),(7,88),(8,87),(9,86),(10,85),(11,97),(12,96),(13,95),(14,94),(15,93),(16,92),(17,91),(18,100),(19,99),(20,98),(21,71),(22,80),(23,79),(24,78),(25,77),(26,76),(27,75),(28,74),(29,73),(30,72),(31,66),(32,65),(33,64),(34,63),(35,62),(36,61),(37,70),(38,69),(39,68),(40,67),(41,56),(42,55),(43,54),(44,53),(45,52),(46,51),(47,60),(48,59),(49,58),(50,57),(101,151),(102,160),(103,159),(104,158),(105,157),(106,156),(107,155),(108,154),(109,153),(110,152),(111,146),(112,145),(113,144),(114,143),(115,142),(116,141),(117,150),(118,149),(119,148),(120,147),(121,136),(122,135),(123,134),(124,133),(125,132),(126,131),(127,140),(128,139),(129,138),(130,137)], [(1,125,25,118),(2,126,26,119),(3,127,27,120),(4,128,28,111),(5,129,29,112),(6,130,30,113),(7,121,21,114),(8,122,22,115),(9,123,23,116),(10,124,24,117),(11,58,158,65),(12,59,159,66),(13,60,160,67),(14,51,151,68),(15,52,152,69),(16,53,153,70),(17,54,154,61),(18,55,155,62),(19,56,156,63),(20,57,157,64),(31,91,48,108),(32,92,49,109),(33,93,50,110),(34,94,41,101),(35,95,42,102),(36,96,43,103),(37,97,44,104),(38,98,45,105),(39,99,46,106),(40,100,47,107),(71,148,88,131),(72,149,89,132),(73,150,90,133),(74,141,81,134),(75,142,82,135),(76,143,83,136),(77,144,84,137),(78,145,85,138),(79,146,86,139),(80,147,87,140)], [(1,16,6,11),(2,17,7,12),(3,18,8,13),(4,19,9,14),(5,20,10,15),(21,159,26,154),(22,160,27,155),(23,151,28,156),(24,152,29,157),(25,153,30,158),(31,136,36,131),(32,137,37,132),(33,138,38,133),(34,139,39,134),(35,140,40,135),(41,146,46,141),(42,147,47,142),(43,148,48,143),(44,149,49,144),(45,150,50,145),(51,111,56,116),(52,112,57,117),(53,113,58,118),(54,114,59,119),(55,115,60,120),(61,121,66,126),(62,122,67,127),(63,123,68,128),(64,124,69,129),(65,125,70,130),(71,108,76,103),(72,109,77,104),(73,110,78,105),(74,101,79,106),(75,102,80,107),(81,94,86,99),(82,95,87,100),(83,96,88,91),(84,97,89,92),(85,98,90,93)]])
68 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 5A | 5B | 10A | ··· | 10N | 20A | ··· | 20X |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 10 | 10 | 10 | 10 | 20 | 20 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 10 | 10 | 10 | 10 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D5 | C4○D4 | D10 | D10 | C4○D20 | D4×D5 | Q8⋊2D5 |
| kernel | C2×D10.13D4 | D10.13D4 | C2×C10.D4 | C2×D10⋊C4 | C10×C4⋊C4 | D5×C22×C4 | C22×D20 | C22×D5 | C2×C4⋊C4 | C2×C10 | C4⋊C4 | C22×C4 | C22 | C22 | C22 |
| # reps | 1 | 8 | 1 | 3 | 1 | 1 | 1 | 4 | 2 | 8 | 8 | 6 | 16 | 4 | 4 |
Matrix representation of C2×D10.13D4 ►in GL5(𝔽41)
| 40 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 34 | 7 | 0 | 0 |
| 0 | 34 | 1 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 11 | 32 | 0 | 0 |
| 0 | 27 | 30 | 0 | 0 |
| 0 | 0 | 0 | 10 | 10 |
| 0 | 0 | 0 | 27 | 31 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 17 | 1 | 0 | 0 |
| 0 | 40 | 24 | 0 | 0 |
| 0 | 0 | 0 | 32 | 0 |
| 0 | 0 | 0 | 18 | 9 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 30 | 9 | 0 | 0 |
| 0 | 32 | 11 | 0 | 0 |
| 0 | 0 | 0 | 31 | 31 |
| 0 | 0 | 0 | 6 | 10 |
G:=sub<GL(5,GF(41))| [40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,34,34,0,0,0,7,1,0,0,0,0,0,40,0,0,0,0,0,40],[40,0,0,0,0,0,11,27,0,0,0,32,30,0,0,0,0,0,10,27,0,0,0,10,31],[40,0,0,0,0,0,17,40,0,0,0,1,24,0,0,0,0,0,32,18,0,0,0,0,9],[40,0,0,0,0,0,30,32,0,0,0,9,11,0,0,0,0,0,31,6,0,0,0,31,10] >;
C2×D10.13D4 in GAP, Magma, Sage, TeX
C_2\times D_{10}._{13}D_4 % in TeX
G:=Group("C2xD10.13D4"); // GroupNames label
G:=SmallGroup(320,1177);
// by ID
G=gap.SmallGroup(320,1177);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,100,675,297,136,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^10=c^2=d^4=1,e^2=b^5,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^-1,b*d=d*b,b*e=e*b,d*c*d^-1=e*c*e^-1=b^5*c,e*d*e^-1=d^-1>;
// generators/relations