direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D4×Dic5, C24.57D10, C10⋊6(C4×D4), (D4×C10)⋊23C4, C20⋊7(C22×C4), C23⋊4(C2×Dic5), C4⋊1(C22×Dic5), (C2×D4).250D10, C10.65(C23×C4), C4⋊Dic5⋊75C22, (C23×Dic5)⋊7C2, (C22×D4).13D5, C22.145(D4×D5), C2.6(C23×Dic5), (C2×C10).290C24, (C2×C20).539C23, (C4×Dic5)⋊66C22, C10.128(C22×D4), (C22×C4).377D10, C23.D5⋊56C22, C22⋊1(C22×Dic5), C22.44(C23×D5), (D4×C10).268C22, (C23×C10).72C22, C23.203(C22×D5), C22.76(D4⋊2D5), (C22×C10).226C23, (C22×C20).272C22, (C2×Dic5).290C23, (C22×Dic5)⋊47C22, C5⋊7(C2×C4×D4), C2.6(C2×D4×D5), (D4×C2×C10).7C2, (C2×C20)⋊27(C2×C4), (C5×D4)⋊29(C2×C4), (C2×C4×Dic5)⋊10C2, (C2×C4)⋊7(C2×Dic5), (C2×C4⋊Dic5)⋊44C2, (C2×C10)⋊7(C22×C4), C2.6(C2×D4⋊2D5), (C22×C10)⋊18(C2×C4), C10.102(C2×C4○D4), (C2×C10).404(C2×D4), (C2×C23.D5)⋊23C2, (C2×C4).622(C22×D5), (C2×C10).174(C4○D4), SmallGroup(320,1467)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D4×Dic5
G = < a,b,c,d,e | a2=b4=c2=d10=1, e2=d5, ab=ba, ac=ca, ad=da, ae=ea, cbc=b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >
Subgroups: 1102 in 426 conjugacy classes, 215 normal (21 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, C23, C23, C23, C10, C10, C10, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C24, Dic5, Dic5, C20, C2×C10, C2×C10, C2×C10, C2×C42, C2×C22⋊C4, C2×C4⋊C4, C4×D4, C23×C4, C22×D4, C2×Dic5, C2×Dic5, C2×C20, C5×D4, C22×C10, C22×C10, C22×C10, C2×C4×D4, C4×Dic5, C4⋊Dic5, C23.D5, C22×Dic5, C22×Dic5, C22×Dic5, C22×C20, D4×C10, C23×C10, C2×C4×Dic5, C2×C4⋊Dic5, D4×Dic5, C2×C23.D5, C23×Dic5, D4×C2×C10, C2×D4×Dic5
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D5, C22×C4, C2×D4, C4○D4, C24, Dic5, D10, C4×D4, C23×C4, C22×D4, C2×C4○D4, C2×Dic5, C22×D5, C2×C4×D4, D4×D5, D4⋊2D5, C22×Dic5, C23×D5, D4×Dic5, C2×D4×D5, C2×D4⋊2D5, C23×Dic5, C2×D4×Dic5
►On 160 points
Generators in S160
(1 68)(2 69)(3 70)(4 61)(5 62)(6 63)(7 64)(8 65)(9 66)(10 67)(11 122)(12 123)(13 124)(14 125)(15 126)(16 127)(17 128)(18 129)(19 130)(20 121)(21 59)(22 60)(23 51)(24 52)(25 53)(26 54)(27 55)(28 56)(29 57)(30 58)(31 71)(32 72)(33 73)(34 74)(35 75)(36 76)(37 77)(38 78)(39 79)(40 80)(41 88)(42 89)(43 90)(44 81)(45 82)(46 83)(47 84)(48 85)(49 86)(50 87)(91 144)(92 145)(93 146)(94 147)(95 148)(96 149)(97 150)(98 141)(99 142)(100 143)(101 138)(102 139)(103 140)(104 131)(105 132)(106 133)(107 134)(108 135)(109 136)(110 137)(111 151)(112 152)(113 153)(114 154)(115 155)(116 156)(117 157)(118 158)(119 159)(120 160)
(1 85 28 76)(2 86 29 77)(3 87 30 78)(4 88 21 79)(5 89 22 80)(6 90 23 71)(7 81 24 72)(8 82 25 73)(9 83 26 74)(10 84 27 75)(11 102 159 99)(12 103 160 100)(13 104 151 91)(14 105 152 92)(15 106 153 93)(16 107 154 94)(17 108 155 95)(18 109 156 96)(19 110 157 97)(20 101 158 98)(31 63 43 51)(32 64 44 52)(33 65 45 53)(34 66 46 54)(35 67 47 55)(36 68 48 56)(37 69 49 57)(38 70 50 58)(39 61 41 59)(40 62 42 60)(111 144 124 131)(112 145 125 132)(113 146 126 133)(114 147 127 134)(115 148 128 135)(116 149 129 136)(117 150 130 137)(118 141 121 138)(119 142 122 139)(120 143 123 140)
(1 51)(2 52)(3 53)(4 54)(5 55)(6 56)(7 57)(8 58)(9 59)(10 60)(11 127)(12 128)(13 129)(14 130)(15 121)(16 122)(17 123)(18 124)(19 125)(20 126)(21 66)(22 67)(23 68)(24 69)(25 70)(26 61)(27 62)(28 63)(29 64)(30 65)(31 76)(32 77)(33 78)(34 79)(35 80)(36 71)(37 72)(38 73)(39 74)(40 75)(41 83)(42 84)(43 85)(44 86)(45 87)(46 88)(47 89)(48 90)(49 81)(50 82)(91 136)(92 137)(93 138)(94 139)(95 140)(96 131)(97 132)(98 133)(99 134)(100 135)(101 146)(102 147)(103 148)(104 149)(105 150)(106 141)(107 142)(108 143)(109 144)(110 145)(111 156)(112 157)(113 158)(114 159)(115 160)(116 151)(117 152)(118 153)(119 154)(120 155)
(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)
(1 139 6 134)(2 138 7 133)(3 137 8 132)(4 136 9 131)(5 135 10 140)(11 31 16 36)(12 40 17 35)(13 39 18 34)(14 38 19 33)(15 37 20 32)(21 149 26 144)(22 148 27 143)(23 147 28 142)(24 146 29 141)(25 145 30 150)(41 156 46 151)(42 155 47 160)(43 154 48 159)(44 153 49 158)(45 152 50 157)(51 94 56 99)(52 93 57 98)(53 92 58 97)(54 91 59 96)(55 100 60 95)(61 109 66 104)(62 108 67 103)(63 107 68 102)(64 106 69 101)(65 105 70 110)(71 127 76 122)(72 126 77 121)(73 125 78 130)(74 124 79 129)(75 123 80 128)(81 113 86 118)(82 112 87 117)(83 111 88 116)(84 120 89 115)(85 119 90 114)
G:=sub<Sym(160)| (1,68)(2,69)(3,70)(4,61)(5,62)(6,63)(7,64)(8,65)(9,66)(10,67)(11,122)(12,123)(13,124)(14,125)(15,126)(16,127)(17,128)(18,129)(19,130)(20,121)(21,59)(22,60)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,88)(42,89)(43,90)(44,81)(45,82)(46,83)(47,84)(48,85)(49,86)(50,87)(91,144)(92,145)(93,146)(94,147)(95,148)(96,149)(97,150)(98,141)(99,142)(100,143)(101,138)(102,139)(103,140)(104,131)(105,132)(106,133)(107,134)(108,135)(109,136)(110,137)(111,151)(112,152)(113,153)(114,154)(115,155)(116,156)(117,157)(118,158)(119,159)(120,160), (1,85,28,76)(2,86,29,77)(3,87,30,78)(4,88,21,79)(5,89,22,80)(6,90,23,71)(7,81,24,72)(8,82,25,73)(9,83,26,74)(10,84,27,75)(11,102,159,99)(12,103,160,100)(13,104,151,91)(14,105,152,92)(15,106,153,93)(16,107,154,94)(17,108,155,95)(18,109,156,96)(19,110,157,97)(20,101,158,98)(31,63,43,51)(32,64,44,52)(33,65,45,53)(34,66,46,54)(35,67,47,55)(36,68,48,56)(37,69,49,57)(38,70,50,58)(39,61,41,59)(40,62,42,60)(111,144,124,131)(112,145,125,132)(113,146,126,133)(114,147,127,134)(115,148,128,135)(116,149,129,136)(117,150,130,137)(118,141,121,138)(119,142,122,139)(120,143,123,140), (1,51)(2,52)(3,53)(4,54)(5,55)(6,56)(7,57)(8,58)(9,59)(10,60)(11,127)(12,128)(13,129)(14,130)(15,121)(16,122)(17,123)(18,124)(19,125)(20,126)(21,66)(22,67)(23,68)(24,69)(25,70)(26,61)(27,62)(28,63)(29,64)(30,65)(31,76)(32,77)(33,78)(34,79)(35,80)(36,71)(37,72)(38,73)(39,74)(40,75)(41,83)(42,84)(43,85)(44,86)(45,87)(46,88)(47,89)(48,90)(49,81)(50,82)(91,136)(92,137)(93,138)(94,139)(95,140)(96,131)(97,132)(98,133)(99,134)(100,135)(101,146)(102,147)(103,148)(104,149)(105,150)(106,141)(107,142)(108,143)(109,144)(110,145)(111,156)(112,157)(113,158)(114,159)(115,160)(116,151)(117,152)(118,153)(119,154)(120,155), (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), (1,139,6,134)(2,138,7,133)(3,137,8,132)(4,136,9,131)(5,135,10,140)(11,31,16,36)(12,40,17,35)(13,39,18,34)(14,38,19,33)(15,37,20,32)(21,149,26,144)(22,148,27,143)(23,147,28,142)(24,146,29,141)(25,145,30,150)(41,156,46,151)(42,155,47,160)(43,154,48,159)(44,153,49,158)(45,152,50,157)(51,94,56,99)(52,93,57,98)(53,92,58,97)(54,91,59,96)(55,100,60,95)(61,109,66,104)(62,108,67,103)(63,107,68,102)(64,106,69,101)(65,105,70,110)(71,127,76,122)(72,126,77,121)(73,125,78,130)(74,124,79,129)(75,123,80,128)(81,113,86,118)(82,112,87,117)(83,111,88,116)(84,120,89,115)(85,119,90,114)>;
G:=Group( (1,68)(2,69)(3,70)(4,61)(5,62)(6,63)(7,64)(8,65)(9,66)(10,67)(11,122)(12,123)(13,124)(14,125)(15,126)(16,127)(17,128)(18,129)(19,130)(20,121)(21,59)(22,60)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,88)(42,89)(43,90)(44,81)(45,82)(46,83)(47,84)(48,85)(49,86)(50,87)(91,144)(92,145)(93,146)(94,147)(95,148)(96,149)(97,150)(98,141)(99,142)(100,143)(101,138)(102,139)(103,140)(104,131)(105,132)(106,133)(107,134)(108,135)(109,136)(110,137)(111,151)(112,152)(113,153)(114,154)(115,155)(116,156)(117,157)(118,158)(119,159)(120,160), (1,85,28,76)(2,86,29,77)(3,87,30,78)(4,88,21,79)(5,89,22,80)(6,90,23,71)(7,81,24,72)(8,82,25,73)(9,83,26,74)(10,84,27,75)(11,102,159,99)(12,103,160,100)(13,104,151,91)(14,105,152,92)(15,106,153,93)(16,107,154,94)(17,108,155,95)(18,109,156,96)(19,110,157,97)(20,101,158,98)(31,63,43,51)(32,64,44,52)(33,65,45,53)(34,66,46,54)(35,67,47,55)(36,68,48,56)(37,69,49,57)(38,70,50,58)(39,61,41,59)(40,62,42,60)(111,144,124,131)(112,145,125,132)(113,146,126,133)(114,147,127,134)(115,148,128,135)(116,149,129,136)(117,150,130,137)(118,141,121,138)(119,142,122,139)(120,143,123,140), (1,51)(2,52)(3,53)(4,54)(5,55)(6,56)(7,57)(8,58)(9,59)(10,60)(11,127)(12,128)(13,129)(14,130)(15,121)(16,122)(17,123)(18,124)(19,125)(20,126)(21,66)(22,67)(23,68)(24,69)(25,70)(26,61)(27,62)(28,63)(29,64)(30,65)(31,76)(32,77)(33,78)(34,79)(35,80)(36,71)(37,72)(38,73)(39,74)(40,75)(41,83)(42,84)(43,85)(44,86)(45,87)(46,88)(47,89)(48,90)(49,81)(50,82)(91,136)(92,137)(93,138)(94,139)(95,140)(96,131)(97,132)(98,133)(99,134)(100,135)(101,146)(102,147)(103,148)(104,149)(105,150)(106,141)(107,142)(108,143)(109,144)(110,145)(111,156)(112,157)(113,158)(114,159)(115,160)(116,151)(117,152)(118,153)(119,154)(120,155), (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), (1,139,6,134)(2,138,7,133)(3,137,8,132)(4,136,9,131)(5,135,10,140)(11,31,16,36)(12,40,17,35)(13,39,18,34)(14,38,19,33)(15,37,20,32)(21,149,26,144)(22,148,27,143)(23,147,28,142)(24,146,29,141)(25,145,30,150)(41,156,46,151)(42,155,47,160)(43,154,48,159)(44,153,49,158)(45,152,50,157)(51,94,56,99)(52,93,57,98)(53,92,58,97)(54,91,59,96)(55,100,60,95)(61,109,66,104)(62,108,67,103)(63,107,68,102)(64,106,69,101)(65,105,70,110)(71,127,76,122)(72,126,77,121)(73,125,78,130)(74,124,79,129)(75,123,80,128)(81,113,86,118)(82,112,87,117)(83,111,88,116)(84,120,89,115)(85,119,90,114) );
G=PermutationGroup([[(1,68),(2,69),(3,70),(4,61),(5,62),(6,63),(7,64),(8,65),(9,66),(10,67),(11,122),(12,123),(13,124),(14,125),(15,126),(16,127),(17,128),(18,129),(19,130),(20,121),(21,59),(22,60),(23,51),(24,52),(25,53),(26,54),(27,55),(28,56),(29,57),(30,58),(31,71),(32,72),(33,73),(34,74),(35,75),(36,76),(37,77),(38,78),(39,79),(40,80),(41,88),(42,89),(43,90),(44,81),(45,82),(46,83),(47,84),(48,85),(49,86),(50,87),(91,144),(92,145),(93,146),(94,147),(95,148),(96,149),(97,150),(98,141),(99,142),(100,143),(101,138),(102,139),(103,140),(104,131),(105,132),(106,133),(107,134),(108,135),(109,136),(110,137),(111,151),(112,152),(113,153),(114,154),(115,155),(116,156),(117,157),(118,158),(119,159),(120,160)], [(1,85,28,76),(2,86,29,77),(3,87,30,78),(4,88,21,79),(5,89,22,80),(6,90,23,71),(7,81,24,72),(8,82,25,73),(9,83,26,74),(10,84,27,75),(11,102,159,99),(12,103,160,100),(13,104,151,91),(14,105,152,92),(15,106,153,93),(16,107,154,94),(17,108,155,95),(18,109,156,96),(19,110,157,97),(20,101,158,98),(31,63,43,51),(32,64,44,52),(33,65,45,53),(34,66,46,54),(35,67,47,55),(36,68,48,56),(37,69,49,57),(38,70,50,58),(39,61,41,59),(40,62,42,60),(111,144,124,131),(112,145,125,132),(113,146,126,133),(114,147,127,134),(115,148,128,135),(116,149,129,136),(117,150,130,137),(118,141,121,138),(119,142,122,139),(120,143,123,140)], [(1,51),(2,52),(3,53),(4,54),(5,55),(6,56),(7,57),(8,58),(9,59),(10,60),(11,127),(12,128),(13,129),(14,130),(15,121),(16,122),(17,123),(18,124),(19,125),(20,126),(21,66),(22,67),(23,68),(24,69),(25,70),(26,61),(27,62),(28,63),(29,64),(30,65),(31,76),(32,77),(33,78),(34,79),(35,80),(36,71),(37,72),(38,73),(39,74),(40,75),(41,83),(42,84),(43,85),(44,86),(45,87),(46,88),(47,89),(48,90),(49,81),(50,82),(91,136),(92,137),(93,138),(94,139),(95,140),(96,131),(97,132),(98,133),(99,134),(100,135),(101,146),(102,147),(103,148),(104,149),(105,150),(106,141),(107,142),(108,143),(109,144),(110,145),(111,156),(112,157),(113,158),(114,159),(115,160),(116,151),(117,152),(118,153),(119,154),(120,155)], [(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)], [(1,139,6,134),(2,138,7,133),(3,137,8,132),(4,136,9,131),(5,135,10,140),(11,31,16,36),(12,40,17,35),(13,39,18,34),(14,38,19,33),(15,37,20,32),(21,149,26,144),(22,148,27,143),(23,147,28,142),(24,146,29,141),(25,145,30,150),(41,156,46,151),(42,155,47,160),(43,154,48,159),(44,153,49,158),(45,152,50,157),(51,94,56,99),(52,93,57,98),(53,92,58,97),(54,91,59,96),(55,100,60,95),(61,109,66,104),(62,108,67,103),(63,107,68,102),(64,106,69,101),(65,105,70,110),(71,127,76,122),(72,126,77,121),(73,125,78,130),(74,124,79,129),(75,123,80,128),(81,113,86,118),(82,112,87,117),(83,111,88,116),(84,120,89,115),(85,119,90,114)]])
80 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | ··· | 2O | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 4M | ··· | 4X | 5A | 5B | 10A | ··· | 10N | 10O | ··· | 10AD | 20A | ··· | 20H |
| order | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 5 | ··· | 5 | 10 | ··· | 10 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
80 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D5 | C4○D4 | D10 | Dic5 | D10 | D10 | D4×D5 | D4⋊2D5 |
| kernel | C2×D4×Dic5 | C2×C4×Dic5 | C2×C4⋊Dic5 | D4×Dic5 | C2×C23.D5 | C23×Dic5 | D4×C2×C10 | D4×C10 | C2×Dic5 | C22×D4 | C2×C10 | C22×C4 | C2×D4 | C2×D4 | C24 | C22 | C22 |
| # reps | 1 | 1 | 1 | 8 | 2 | 2 | 1 | 16 | 4 | 2 | 4 | 2 | 16 | 8 | 4 | 4 | 4 |
Matrix representation of C2×D4×Dic5 ►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 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 37 |
| 0 | 0 | 0 | 0 | 21 | 1 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 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 | 20 | 40 |
| 23 | 0 | 0 | 0 | 0 | 0 |
| 0 | 25 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 1 | 35 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 31 | 0 | 0 |
| 0 | 0 | 14 | 37 | 0 | 0 |
| 0 | 0 | 0 | 0 | 32 | 0 |
| 0 | 0 | 0 | 0 | 0 | 32 |
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],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,21,0,0,0,0,37,1],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,20,0,0,0,0,0,40],[23,0,0,0,0,0,0,25,0,0,0,0,0,0,0,1,0,0,0,0,40,35,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[0,40,0,0,0,0,1,0,0,0,0,0,0,0,4,14,0,0,0,0,31,37,0,0,0,0,0,0,32,0,0,0,0,0,0,32] >;
C2×D4×Dic5 in GAP, Magma, Sage, TeX
C_2\times D_4\times {\rm Dic}_5 % in TeX
G:=Group("C2xD4xDic5"); // GroupNames label
G:=SmallGroup(320,1467);
// by ID
G=gap.SmallGroup(320,1467);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,297,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=c^2=d^10=1,e^2=d^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,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations