direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D5×C2.D8, D10.23D8, D10.12Q16, (C8×D5)⋊1C4, C8⋊13(C4×D5), C2.4(D5×D8), C40⋊15(C2×C4), C2.4(D5×Q16), C4.29(Q8×D5), C40⋊5C4⋊20C2, C10.28(C2×D8), (C4×D5).15Q8, C20.20(C2×Q8), C4⋊C4.169D10, (C2×C8).229D10, C10.23(C2×Q16), C22.89(D4×D5), D10.37(C4⋊C4), C10.D8⋊19C2, (C2×C40).81C22, Dic5.17(C4⋊C4), (C2×C20).295C23, C20.107(C22×C4), (C2×Dic5).147D4, (C22×D5).155D4, C4⋊Dic5.121C22, C5⋊2(C2×C2.D8), (D5×C2×C8).2C2, C4.79(C2×C4×D5), (D5×C4⋊C4).7C2, C2.14(D5×C4⋊C4), (C5×C2.D8)⋊3C2, C5⋊2C8⋊28(C2×C4), C10.36(C2×C4⋊C4), (C4×D5).75(C2×C4), (C2×C10).300(C2×D4), (C5×C4⋊C4).88C22, (C2×C4×D5).304C22, (C2×C4).398(C22×D5), (C2×C5⋊2C8).241C22, SmallGroup(320,506)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D5×C2.D8
G = < a,b,c,d,e | a5=b2=c2=d8=1, e2=c, bab=a-1, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >
Subgroups: 478 in 130 conjugacy classes, 63 normal (27 characteristic)
C1, C2, C2, C4, C4, C22, C22, C5, C8, C8, C2×C4, C2×C4, C23, D5, C10, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, Dic5, Dic5, C20, C20, D10, C2×C10, C2.D8, C2.D8, C2×C4⋊C4, C22×C8, C5⋊2C8, C40, C4×D5, C4×D5, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×D5, C2×C2.D8, C8×D5, C2×C5⋊2C8, C10.D4, C4⋊Dic5, C5×C4⋊C4, C2×C40, C2×C4×D5, C2×C4×D5, C10.D8, C40⋊5C4, C5×C2.D8, D5×C4⋊C4, D5×C2×C8, D5×C2.D8
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D5, C4⋊C4, D8, Q16, C22×C4, C2×D4, C2×Q8, D10, C2.D8, C2×C4⋊C4, C2×D8, C2×Q16, C4×D5, C22×D5, C2×C2.D8, C2×C4×D5, D4×D5, Q8×D5, D5×C4⋊C4, D5×D8, D5×Q16, D5×C2.D8
►On 160 points
Generators in S160
(1 113 21 133 99)(2 114 22 134 100)(3 115 23 135 101)(4 116 24 136 102)(5 117 17 129 103)(6 118 18 130 104)(7 119 19 131 97)(8 120 20 132 98)(9 49 93 81 124)(10 50 94 82 125)(11 51 95 83 126)(12 52 96 84 127)(13 53 89 85 128)(14 54 90 86 121)(15 55 91 87 122)(16 56 92 88 123)(25 70 107 146 137)(26 71 108 147 138)(27 72 109 148 139)(28 65 110 149 140)(29 66 111 150 141)(30 67 112 151 142)(31 68 105 152 143)(32 69 106 145 144)(33 74 58 160 45)(34 75 59 153 46)(35 76 60 154 47)(36 77 61 155 48)(37 78 62 156 41)(38 79 63 157 42)(39 80 64 158 43)(40 73 57 159 44)
(1 103)(2 104)(3 97)(4 98)(5 99)(6 100)(7 101)(8 102)(9 53)(10 54)(11 55)(12 56)(13 49)(14 50)(15 51)(16 52)(17 21)(18 22)(19 23)(20 24)(25 150)(26 151)(27 152)(28 145)(29 146)(30 147)(31 148)(32 149)(33 37)(34 38)(35 39)(36 40)(41 74)(42 75)(43 76)(44 77)(45 78)(46 79)(47 80)(48 73)(57 155)(58 156)(59 157)(60 158)(61 159)(62 160)(63 153)(64 154)(65 106)(66 107)(67 108)(68 109)(69 110)(70 111)(71 112)(72 105)(81 85)(82 86)(83 87)(84 88)(89 124)(90 125)(91 126)(92 127)(93 128)(94 121)(95 122)(96 123)(113 129)(114 130)(115 131)(116 132)(117 133)(118 134)(119 135)(120 136)(137 141)(138 142)(139 143)(140 144)
(1 105)(2 106)(3 107)(4 108)(5 109)(6 110)(7 111)(8 112)(9 63)(10 64)(11 57)(12 58)(13 59)(14 60)(15 61)(16 62)(17 139)(18 140)(19 141)(20 142)(21 143)(22 144)(23 137)(24 138)(25 135)(26 136)(27 129)(28 130)(29 131)(30 132)(31 133)(32 134)(33 84)(34 85)(35 86)(36 87)(37 88)(38 81)(39 82)(40 83)(41 92)(42 93)(43 94)(44 95)(45 96)(46 89)(47 90)(48 91)(49 157)(50 158)(51 159)(52 160)(53 153)(54 154)(55 155)(56 156)(65 104)(66 97)(67 98)(68 99)(69 100)(70 101)(71 102)(72 103)(73 126)(74 127)(75 128)(76 121)(77 122)(78 123)(79 124)(80 125)(113 152)(114 145)(115 146)(116 147)(117 148)(118 149)(119 150)(120 151)
(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 54 105 154)(2 53 106 153)(3 52 107 160)(4 51 108 159)(5 50 109 158)(6 49 110 157)(7 56 111 156)(8 55 112 155)(9 65 63 104)(10 72 64 103)(11 71 57 102)(12 70 58 101)(13 69 59 100)(14 68 60 99)(15 67 61 98)(16 66 62 97)(17 82 139 39)(18 81 140 38)(19 88 141 37)(20 87 142 36)(21 86 143 35)(22 85 144 34)(23 84 137 33)(24 83 138 40)(25 74 135 127)(26 73 136 126)(27 80 129 125)(28 79 130 124)(29 78 131 123)(30 77 132 122)(31 76 133 121)(32 75 134 128)(41 119 92 150)(42 118 93 149)(43 117 94 148)(44 116 95 147)(45 115 96 146)(46 114 89 145)(47 113 90 152)(48 120 91 151)
G:=sub<Sym(160)| (1,113,21,133,99)(2,114,22,134,100)(3,115,23,135,101)(4,116,24,136,102)(5,117,17,129,103)(6,118,18,130,104)(7,119,19,131,97)(8,120,20,132,98)(9,49,93,81,124)(10,50,94,82,125)(11,51,95,83,126)(12,52,96,84,127)(13,53,89,85,128)(14,54,90,86,121)(15,55,91,87,122)(16,56,92,88,123)(25,70,107,146,137)(26,71,108,147,138)(27,72,109,148,139)(28,65,110,149,140)(29,66,111,150,141)(30,67,112,151,142)(31,68,105,152,143)(32,69,106,145,144)(33,74,58,160,45)(34,75,59,153,46)(35,76,60,154,47)(36,77,61,155,48)(37,78,62,156,41)(38,79,63,157,42)(39,80,64,158,43)(40,73,57,159,44), (1,103)(2,104)(3,97)(4,98)(5,99)(6,100)(7,101)(8,102)(9,53)(10,54)(11,55)(12,56)(13,49)(14,50)(15,51)(16,52)(17,21)(18,22)(19,23)(20,24)(25,150)(26,151)(27,152)(28,145)(29,146)(30,147)(31,148)(32,149)(33,37)(34,38)(35,39)(36,40)(41,74)(42,75)(43,76)(44,77)(45,78)(46,79)(47,80)(48,73)(57,155)(58,156)(59,157)(60,158)(61,159)(62,160)(63,153)(64,154)(65,106)(66,107)(67,108)(68,109)(69,110)(70,111)(71,112)(72,105)(81,85)(82,86)(83,87)(84,88)(89,124)(90,125)(91,126)(92,127)(93,128)(94,121)(95,122)(96,123)(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)(120,136)(137,141)(138,142)(139,143)(140,144), (1,105)(2,106)(3,107)(4,108)(5,109)(6,110)(7,111)(8,112)(9,63)(10,64)(11,57)(12,58)(13,59)(14,60)(15,61)(16,62)(17,139)(18,140)(19,141)(20,142)(21,143)(22,144)(23,137)(24,138)(25,135)(26,136)(27,129)(28,130)(29,131)(30,132)(31,133)(32,134)(33,84)(34,85)(35,86)(36,87)(37,88)(38,81)(39,82)(40,83)(41,92)(42,93)(43,94)(44,95)(45,96)(46,89)(47,90)(48,91)(49,157)(50,158)(51,159)(52,160)(53,153)(54,154)(55,155)(56,156)(65,104)(66,97)(67,98)(68,99)(69,100)(70,101)(71,102)(72,103)(73,126)(74,127)(75,128)(76,121)(77,122)(78,123)(79,124)(80,125)(113,152)(114,145)(115,146)(116,147)(117,148)(118,149)(119,150)(120,151), (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), (1,54,105,154)(2,53,106,153)(3,52,107,160)(4,51,108,159)(5,50,109,158)(6,49,110,157)(7,56,111,156)(8,55,112,155)(9,65,63,104)(10,72,64,103)(11,71,57,102)(12,70,58,101)(13,69,59,100)(14,68,60,99)(15,67,61,98)(16,66,62,97)(17,82,139,39)(18,81,140,38)(19,88,141,37)(20,87,142,36)(21,86,143,35)(22,85,144,34)(23,84,137,33)(24,83,138,40)(25,74,135,127)(26,73,136,126)(27,80,129,125)(28,79,130,124)(29,78,131,123)(30,77,132,122)(31,76,133,121)(32,75,134,128)(41,119,92,150)(42,118,93,149)(43,117,94,148)(44,116,95,147)(45,115,96,146)(46,114,89,145)(47,113,90,152)(48,120,91,151)>;
G:=Group( (1,113,21,133,99)(2,114,22,134,100)(3,115,23,135,101)(4,116,24,136,102)(5,117,17,129,103)(6,118,18,130,104)(7,119,19,131,97)(8,120,20,132,98)(9,49,93,81,124)(10,50,94,82,125)(11,51,95,83,126)(12,52,96,84,127)(13,53,89,85,128)(14,54,90,86,121)(15,55,91,87,122)(16,56,92,88,123)(25,70,107,146,137)(26,71,108,147,138)(27,72,109,148,139)(28,65,110,149,140)(29,66,111,150,141)(30,67,112,151,142)(31,68,105,152,143)(32,69,106,145,144)(33,74,58,160,45)(34,75,59,153,46)(35,76,60,154,47)(36,77,61,155,48)(37,78,62,156,41)(38,79,63,157,42)(39,80,64,158,43)(40,73,57,159,44), (1,103)(2,104)(3,97)(4,98)(5,99)(6,100)(7,101)(8,102)(9,53)(10,54)(11,55)(12,56)(13,49)(14,50)(15,51)(16,52)(17,21)(18,22)(19,23)(20,24)(25,150)(26,151)(27,152)(28,145)(29,146)(30,147)(31,148)(32,149)(33,37)(34,38)(35,39)(36,40)(41,74)(42,75)(43,76)(44,77)(45,78)(46,79)(47,80)(48,73)(57,155)(58,156)(59,157)(60,158)(61,159)(62,160)(63,153)(64,154)(65,106)(66,107)(67,108)(68,109)(69,110)(70,111)(71,112)(72,105)(81,85)(82,86)(83,87)(84,88)(89,124)(90,125)(91,126)(92,127)(93,128)(94,121)(95,122)(96,123)(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)(120,136)(137,141)(138,142)(139,143)(140,144), (1,105)(2,106)(3,107)(4,108)(5,109)(6,110)(7,111)(8,112)(9,63)(10,64)(11,57)(12,58)(13,59)(14,60)(15,61)(16,62)(17,139)(18,140)(19,141)(20,142)(21,143)(22,144)(23,137)(24,138)(25,135)(26,136)(27,129)(28,130)(29,131)(30,132)(31,133)(32,134)(33,84)(34,85)(35,86)(36,87)(37,88)(38,81)(39,82)(40,83)(41,92)(42,93)(43,94)(44,95)(45,96)(46,89)(47,90)(48,91)(49,157)(50,158)(51,159)(52,160)(53,153)(54,154)(55,155)(56,156)(65,104)(66,97)(67,98)(68,99)(69,100)(70,101)(71,102)(72,103)(73,126)(74,127)(75,128)(76,121)(77,122)(78,123)(79,124)(80,125)(113,152)(114,145)(115,146)(116,147)(117,148)(118,149)(119,150)(120,151), (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), (1,54,105,154)(2,53,106,153)(3,52,107,160)(4,51,108,159)(5,50,109,158)(6,49,110,157)(7,56,111,156)(8,55,112,155)(9,65,63,104)(10,72,64,103)(11,71,57,102)(12,70,58,101)(13,69,59,100)(14,68,60,99)(15,67,61,98)(16,66,62,97)(17,82,139,39)(18,81,140,38)(19,88,141,37)(20,87,142,36)(21,86,143,35)(22,85,144,34)(23,84,137,33)(24,83,138,40)(25,74,135,127)(26,73,136,126)(27,80,129,125)(28,79,130,124)(29,78,131,123)(30,77,132,122)(31,76,133,121)(32,75,134,128)(41,119,92,150)(42,118,93,149)(43,117,94,148)(44,116,95,147)(45,115,96,146)(46,114,89,145)(47,113,90,152)(48,120,91,151) );
G=PermutationGroup([[(1,113,21,133,99),(2,114,22,134,100),(3,115,23,135,101),(4,116,24,136,102),(5,117,17,129,103),(6,118,18,130,104),(7,119,19,131,97),(8,120,20,132,98),(9,49,93,81,124),(10,50,94,82,125),(11,51,95,83,126),(12,52,96,84,127),(13,53,89,85,128),(14,54,90,86,121),(15,55,91,87,122),(16,56,92,88,123),(25,70,107,146,137),(26,71,108,147,138),(27,72,109,148,139),(28,65,110,149,140),(29,66,111,150,141),(30,67,112,151,142),(31,68,105,152,143),(32,69,106,145,144),(33,74,58,160,45),(34,75,59,153,46),(35,76,60,154,47),(36,77,61,155,48),(37,78,62,156,41),(38,79,63,157,42),(39,80,64,158,43),(40,73,57,159,44)], [(1,103),(2,104),(3,97),(4,98),(5,99),(6,100),(7,101),(8,102),(9,53),(10,54),(11,55),(12,56),(13,49),(14,50),(15,51),(16,52),(17,21),(18,22),(19,23),(20,24),(25,150),(26,151),(27,152),(28,145),(29,146),(30,147),(31,148),(32,149),(33,37),(34,38),(35,39),(36,40),(41,74),(42,75),(43,76),(44,77),(45,78),(46,79),(47,80),(48,73),(57,155),(58,156),(59,157),(60,158),(61,159),(62,160),(63,153),(64,154),(65,106),(66,107),(67,108),(68,109),(69,110),(70,111),(71,112),(72,105),(81,85),(82,86),(83,87),(84,88),(89,124),(90,125),(91,126),(92,127),(93,128),(94,121),(95,122),(96,123),(113,129),(114,130),(115,131),(116,132),(117,133),(118,134),(119,135),(120,136),(137,141),(138,142),(139,143),(140,144)], [(1,105),(2,106),(3,107),(4,108),(5,109),(6,110),(7,111),(8,112),(9,63),(10,64),(11,57),(12,58),(13,59),(14,60),(15,61),(16,62),(17,139),(18,140),(19,141),(20,142),(21,143),(22,144),(23,137),(24,138),(25,135),(26,136),(27,129),(28,130),(29,131),(30,132),(31,133),(32,134),(33,84),(34,85),(35,86),(36,87),(37,88),(38,81),(39,82),(40,83),(41,92),(42,93),(43,94),(44,95),(45,96),(46,89),(47,90),(48,91),(49,157),(50,158),(51,159),(52,160),(53,153),(54,154),(55,155),(56,156),(65,104),(66,97),(67,98),(68,99),(69,100),(70,101),(71,102),(72,103),(73,126),(74,127),(75,128),(76,121),(77,122),(78,123),(79,124),(80,125),(113,152),(114,145),(115,146),(116,147),(117,148),(118,149),(119,150),(120,151)], [(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)], [(1,54,105,154),(2,53,106,153),(3,52,107,160),(4,51,108,159),(5,50,109,158),(6,49,110,157),(7,56,111,156),(8,55,112,155),(9,65,63,104),(10,72,64,103),(11,71,57,102),(12,70,58,101),(13,69,59,100),(14,68,60,99),(15,67,61,98),(16,66,62,97),(17,82,139,39),(18,81,140,38),(19,88,141,37),(20,87,142,36),(21,86,143,35),(22,85,144,34),(23,84,137,33),(24,83,138,40),(25,74,135,127),(26,73,136,126),(27,80,129,125),(28,79,130,124),(29,78,131,123),(30,77,132,122),(31,76,133,121),(32,75,134,128),(41,119,92,150),(42,118,93,149),(43,117,94,148),(44,116,95,147),(45,115,96,146),(46,114,89,145),(47,113,90,152),(48,120,91,151)]])
56 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 5A | 5B | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 10A | ··· | 10F | 20A | 20B | 20C | 20D | 20E | ··· | 20L | 40A | ··· | 40H |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 20 | ··· | 20 | 40 | ··· | 40 |
| size | 1 | 1 | 1 | 1 | 5 | 5 | 5 | 5 | 2 | 2 | 4 | 4 | 4 | 4 | 10 | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | 2 | 2 | 2 | 10 | 10 | 10 | 10 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
56 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | + | - | + | + | - | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | Q8 | D4 | D4 | D5 | D8 | Q16 | D10 | D10 | C4×D5 | Q8×D5 | D4×D5 | D5×D8 | D5×Q16 |
| kernel | D5×C2.D8 | C10.D8 | C40⋊5C4 | C5×C2.D8 | D5×C4⋊C4 | D5×C2×C8 | C8×D5 | C4×D5 | C2×Dic5 | C22×D5 | C2.D8 | D10 | D10 | C4⋊C4 | C2×C8 | C8 | C4 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 1 | 2 | 1 | 8 | 2 | 1 | 1 | 2 | 4 | 4 | 4 | 2 | 8 | 2 | 2 | 4 | 4 |
Matrix representation of D5×C2.D8 ►in GL5(𝔽41)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 40 | 1 | 0 | 0 |
| 0 | 33 | 7 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 33 | 1 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 40 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 29 | 12 |
| 0 | 0 | 0 | 29 | 29 |
| 32 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 14 | 34 |
| 0 | 0 | 0 | 34 | 27 |
G:=sub<GL(5,GF(41))| [1,0,0,0,0,0,40,33,0,0,0,1,7,0,0,0,0,0,1,0,0,0,0,0,1],[40,0,0,0,0,0,40,33,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40],[40,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,29,29,0,0,0,12,29],[32,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,14,34,0,0,0,34,27] >;
D5×C2.D8 in GAP, Magma, Sage, TeX
D_5\times C_2.D_8
% in TeX
G:=Group("D5xC2.D8"); // GroupNames label
G:=SmallGroup(320,506);
// by ID
G=gap.SmallGroup(320,506);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,120,219,58,438,102,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^5=b^2=c^2=d^8=1,e^2=c,b*a*b=a^-1,a*c=c*a,a*d=d*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=d^-1>;
// generators/relations