direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D4⋊Dic5, (D4×C10)⋊17C4, D4⋊3(C2×Dic5), (C2×D4)⋊3Dic5, (C2×C10).47D8, C10.71(C2×D8), (C2×C20).188D4, C20.202(C2×D4), C10⋊4(D4⋊C4), (C22×D4).1D5, (C2×D4).195D10, C4⋊Dic5⋊67C22, (C2×C10).34SD16, C10.63(C2×SD16), C4.7(C23.D5), C4.9(C22×Dic5), C20.77(C22⋊C4), C20.138(C22×C4), (C2×C20).469C23, C22.25(D4⋊D5), (C22×C10).194D4, (C22×C4).352D10, (D4×C10).237C22, C23.100(C5⋊D4), C22.12(D4.D5), (C22×C20).194C22, C22.33(C23.D5), C5⋊5(C2×D4⋊C4), C2.4(C2×D4⋊D5), (D4×C2×C10).1C2, (C5×D4)⋊26(C2×C4), C4.88(C2×C5⋊D4), C2.4(C2×D4.D5), (C2×C4⋊Dic5)⋊34C2, (C22×C5⋊2C8)⋊7C2, (C2×C20).288(C2×C4), (C2×C5⋊2C8)⋊32C22, C2.7(C2×C23.D5), (C2×C10).551(C2×D4), (C2×C4).49(C2×Dic5), C22.89(C2×C5⋊D4), (C2×C4).147(C5⋊D4), C10.112(C2×C22⋊C4), (C2×C4).556(C22×D5), (C2×C10).174(C22⋊C4), SmallGroup(320,841)
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=ebe-1=b-1, bd=db, cd=dc, ece-1=bc, ede-1=d-1 >
Subgroups: 574 in 202 conjugacy classes, 87 normal (27 characteristic)
C1, C2, C2, C2, C4, C4, C4, C22, C22, C22, C5, C8, C2×C4, C2×C4, C2×C4, D4, D4, C23, C23, C10, C10, C10, C4⋊C4, C2×C8, C22×C4, C22×C4, C2×D4, C2×D4, C24, Dic5, C20, C20, C2×C10, C2×C10, C2×C10, D4⋊C4, C2×C4⋊C4, C22×C8, C22×D4, C5⋊2C8, C2×Dic5, C2×C20, C2×C20, C5×D4, C5×D4, C22×C10, C22×C10, C2×D4⋊C4, C2×C5⋊2C8, C2×C5⋊2C8, C4⋊Dic5, C4⋊Dic5, C22×Dic5, C22×C20, D4×C10, D4×C10, C23×C10, D4⋊Dic5, C22×C5⋊2C8, C2×C4⋊Dic5, D4×C2×C10, C2×D4⋊Dic5
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D5, C22⋊C4, D8, SD16, C22×C4, C2×D4, Dic5, D10, D4⋊C4, C2×C22⋊C4, C2×D8, C2×SD16, C2×Dic5, C5⋊D4, C22×D5, C2×D4⋊C4, D4⋊D5, D4.D5, C23.D5, C22×Dic5, C2×C5⋊D4, D4⋊Dic5, C2×D4⋊D5, C2×D4.D5, C2×C23.D5, C2×D4⋊Dic5
►On 160 points
Generators in S160
(1 52)(2 53)(3 54)(4 55)(5 56)(6 57)(7 58)(8 59)(9 60)(10 51)(11 64)(12 65)(13 66)(14 67)(15 68)(16 69)(17 70)(18 61)(19 62)(20 63)(21 123)(22 124)(23 125)(24 126)(25 127)(26 128)(27 129)(28 130)(29 121)(30 122)(31 76)(32 77)(33 78)(34 79)(35 80)(36 71)(37 72)(38 73)(39 74)(40 75)(41 89)(42 90)(43 81)(44 82)(45 83)(46 84)(47 85)(48 86)(49 87)(50 88)(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 47 31 18)(2 48 32 19)(3 49 33 20)(4 50 34 11)(5 41 35 12)(6 42 36 13)(7 43 37 14)(8 44 38 15)(9 45 39 16)(10 46 40 17)(21 138 144 159)(22 139 145 160)(23 140 146 151)(24 131 147 152)(25 132 148 153)(26 133 149 154)(27 134 150 155)(28 135 141 156)(29 136 142 157)(30 137 143 158)(51 84 75 70)(52 85 76 61)(53 86 77 62)(54 87 78 63)(55 88 79 64)(56 89 80 65)(57 90 71 66)(58 81 72 67)(59 82 73 68)(60 83 74 69)(91 107 112 121)(92 108 113 122)(93 109 114 123)(94 110 115 124)(95 101 116 125)(96 102 117 126)(97 103 118 127)(98 104 119 128)(99 105 120 129)(100 106 111 130)
(1 18)(2 19)(3 20)(4 11)(5 12)(6 13)(7 14)(8 15)(9 16)(10 17)(31 47)(32 48)(33 49)(34 50)(35 41)(36 42)(37 43)(38 44)(39 45)(40 46)(51 70)(52 61)(53 62)(54 63)(55 64)(56 65)(57 66)(58 67)(59 68)(60 69)(71 90)(72 81)(73 82)(74 83)(75 84)(76 85)(77 86)(78 87)(79 88)(80 89)(91 112)(92 113)(93 114)(94 115)(95 116)(96 117)(97 118)(98 119)(99 120)(100 111)(131 152)(132 153)(133 154)(134 155)(135 156)(136 157)(137 158)(138 159)(139 160)(140 151)
(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)
(1 133 6 138)(2 132 7 137)(3 131 8 136)(4 140 9 135)(5 139 10 134)(11 146 16 141)(12 145 17 150)(13 144 18 149)(14 143 19 148)(15 142 20 147)(21 47 26 42)(22 46 27 41)(23 45 28 50)(24 44 29 49)(25 43 30 48)(31 154 36 159)(32 153 37 158)(33 152 38 157)(34 151 39 156)(35 160 40 155)(51 99 56 94)(52 98 57 93)(53 97 58 92)(54 96 59 91)(55 95 60 100)(61 104 66 109)(62 103 67 108)(63 102 68 107)(64 101 69 106)(65 110 70 105)(71 114 76 119)(72 113 77 118)(73 112 78 117)(74 111 79 116)(75 120 80 115)(81 122 86 127)(82 121 87 126)(83 130 88 125)(84 129 89 124)(85 128 90 123)
G:=sub<Sym(160)| (1,52)(2,53)(3,54)(4,55)(5,56)(6,57)(7,58)(8,59)(9,60)(10,51)(11,64)(12,65)(13,66)(14,67)(15,68)(16,69)(17,70)(18,61)(19,62)(20,63)(21,123)(22,124)(23,125)(24,126)(25,127)(26,128)(27,129)(28,130)(29,121)(30,122)(31,76)(32,77)(33,78)(34,79)(35,80)(36,71)(37,72)(38,73)(39,74)(40,75)(41,89)(42,90)(43,81)(44,82)(45,83)(46,84)(47,85)(48,86)(49,87)(50,88)(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), (1,47,31,18)(2,48,32,19)(3,49,33,20)(4,50,34,11)(5,41,35,12)(6,42,36,13)(7,43,37,14)(8,44,38,15)(9,45,39,16)(10,46,40,17)(21,138,144,159)(22,139,145,160)(23,140,146,151)(24,131,147,152)(25,132,148,153)(26,133,149,154)(27,134,150,155)(28,135,141,156)(29,136,142,157)(30,137,143,158)(51,84,75,70)(52,85,76,61)(53,86,77,62)(54,87,78,63)(55,88,79,64)(56,89,80,65)(57,90,71,66)(58,81,72,67)(59,82,73,68)(60,83,74,69)(91,107,112,121)(92,108,113,122)(93,109,114,123)(94,110,115,124)(95,101,116,125)(96,102,117,126)(97,103,118,127)(98,104,119,128)(99,105,120,129)(100,106,111,130), (1,18)(2,19)(3,20)(4,11)(5,12)(6,13)(7,14)(8,15)(9,16)(10,17)(31,47)(32,48)(33,49)(34,50)(35,41)(36,42)(37,43)(38,44)(39,45)(40,46)(51,70)(52,61)(53,62)(54,63)(55,64)(56,65)(57,66)(58,67)(59,68)(60,69)(71,90)(72,81)(73,82)(74,83)(75,84)(76,85)(77,86)(78,87)(79,88)(80,89)(91,112)(92,113)(93,114)(94,115)(95,116)(96,117)(97,118)(98,119)(99,120)(100,111)(131,152)(132,153)(133,154)(134,155)(135,156)(136,157)(137,158)(138,159)(139,160)(140,151), (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), (1,133,6,138)(2,132,7,137)(3,131,8,136)(4,140,9,135)(5,139,10,134)(11,146,16,141)(12,145,17,150)(13,144,18,149)(14,143,19,148)(15,142,20,147)(21,47,26,42)(22,46,27,41)(23,45,28,50)(24,44,29,49)(25,43,30,48)(31,154,36,159)(32,153,37,158)(33,152,38,157)(34,151,39,156)(35,160,40,155)(51,99,56,94)(52,98,57,93)(53,97,58,92)(54,96,59,91)(55,95,60,100)(61,104,66,109)(62,103,67,108)(63,102,68,107)(64,101,69,106)(65,110,70,105)(71,114,76,119)(72,113,77,118)(73,112,78,117)(74,111,79,116)(75,120,80,115)(81,122,86,127)(82,121,87,126)(83,130,88,125)(84,129,89,124)(85,128,90,123)>;
G:=Group( (1,52)(2,53)(3,54)(4,55)(5,56)(6,57)(7,58)(8,59)(9,60)(10,51)(11,64)(12,65)(13,66)(14,67)(15,68)(16,69)(17,70)(18,61)(19,62)(20,63)(21,123)(22,124)(23,125)(24,126)(25,127)(26,128)(27,129)(28,130)(29,121)(30,122)(31,76)(32,77)(33,78)(34,79)(35,80)(36,71)(37,72)(38,73)(39,74)(40,75)(41,89)(42,90)(43,81)(44,82)(45,83)(46,84)(47,85)(48,86)(49,87)(50,88)(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), (1,47,31,18)(2,48,32,19)(3,49,33,20)(4,50,34,11)(5,41,35,12)(6,42,36,13)(7,43,37,14)(8,44,38,15)(9,45,39,16)(10,46,40,17)(21,138,144,159)(22,139,145,160)(23,140,146,151)(24,131,147,152)(25,132,148,153)(26,133,149,154)(27,134,150,155)(28,135,141,156)(29,136,142,157)(30,137,143,158)(51,84,75,70)(52,85,76,61)(53,86,77,62)(54,87,78,63)(55,88,79,64)(56,89,80,65)(57,90,71,66)(58,81,72,67)(59,82,73,68)(60,83,74,69)(91,107,112,121)(92,108,113,122)(93,109,114,123)(94,110,115,124)(95,101,116,125)(96,102,117,126)(97,103,118,127)(98,104,119,128)(99,105,120,129)(100,106,111,130), (1,18)(2,19)(3,20)(4,11)(5,12)(6,13)(7,14)(8,15)(9,16)(10,17)(31,47)(32,48)(33,49)(34,50)(35,41)(36,42)(37,43)(38,44)(39,45)(40,46)(51,70)(52,61)(53,62)(54,63)(55,64)(56,65)(57,66)(58,67)(59,68)(60,69)(71,90)(72,81)(73,82)(74,83)(75,84)(76,85)(77,86)(78,87)(79,88)(80,89)(91,112)(92,113)(93,114)(94,115)(95,116)(96,117)(97,118)(98,119)(99,120)(100,111)(131,152)(132,153)(133,154)(134,155)(135,156)(136,157)(137,158)(138,159)(139,160)(140,151), (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), (1,133,6,138)(2,132,7,137)(3,131,8,136)(4,140,9,135)(5,139,10,134)(11,146,16,141)(12,145,17,150)(13,144,18,149)(14,143,19,148)(15,142,20,147)(21,47,26,42)(22,46,27,41)(23,45,28,50)(24,44,29,49)(25,43,30,48)(31,154,36,159)(32,153,37,158)(33,152,38,157)(34,151,39,156)(35,160,40,155)(51,99,56,94)(52,98,57,93)(53,97,58,92)(54,96,59,91)(55,95,60,100)(61,104,66,109)(62,103,67,108)(63,102,68,107)(64,101,69,106)(65,110,70,105)(71,114,76,119)(72,113,77,118)(73,112,78,117)(74,111,79,116)(75,120,80,115)(81,122,86,127)(82,121,87,126)(83,130,88,125)(84,129,89,124)(85,128,90,123) );
G=PermutationGroup([[(1,52),(2,53),(3,54),(4,55),(5,56),(6,57),(7,58),(8,59),(9,60),(10,51),(11,64),(12,65),(13,66),(14,67),(15,68),(16,69),(17,70),(18,61),(19,62),(20,63),(21,123),(22,124),(23,125),(24,126),(25,127),(26,128),(27,129),(28,130),(29,121),(30,122),(31,76),(32,77),(33,78),(34,79),(35,80),(36,71),(37,72),(38,73),(39,74),(40,75),(41,89),(42,90),(43,81),(44,82),(45,83),(46,84),(47,85),(48,86),(49,87),(50,88),(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)], [(1,47,31,18),(2,48,32,19),(3,49,33,20),(4,50,34,11),(5,41,35,12),(6,42,36,13),(7,43,37,14),(8,44,38,15),(9,45,39,16),(10,46,40,17),(21,138,144,159),(22,139,145,160),(23,140,146,151),(24,131,147,152),(25,132,148,153),(26,133,149,154),(27,134,150,155),(28,135,141,156),(29,136,142,157),(30,137,143,158),(51,84,75,70),(52,85,76,61),(53,86,77,62),(54,87,78,63),(55,88,79,64),(56,89,80,65),(57,90,71,66),(58,81,72,67),(59,82,73,68),(60,83,74,69),(91,107,112,121),(92,108,113,122),(93,109,114,123),(94,110,115,124),(95,101,116,125),(96,102,117,126),(97,103,118,127),(98,104,119,128),(99,105,120,129),(100,106,111,130)], [(1,18),(2,19),(3,20),(4,11),(5,12),(6,13),(7,14),(8,15),(9,16),(10,17),(31,47),(32,48),(33,49),(34,50),(35,41),(36,42),(37,43),(38,44),(39,45),(40,46),(51,70),(52,61),(53,62),(54,63),(55,64),(56,65),(57,66),(58,67),(59,68),(60,69),(71,90),(72,81),(73,82),(74,83),(75,84),(76,85),(77,86),(78,87),(79,88),(80,89),(91,112),(92,113),(93,114),(94,115),(95,116),(96,117),(97,118),(98,119),(99,120),(100,111),(131,152),(132,153),(133,154),(134,155),(135,156),(136,157),(137,158),(138,159),(139,160),(140,151)], [(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)], [(1,133,6,138),(2,132,7,137),(3,131,8,136),(4,140,9,135),(5,139,10,134),(11,146,16,141),(12,145,17,150),(13,144,18,149),(14,143,19,148),(15,142,20,147),(21,47,26,42),(22,46,27,41),(23,45,28,50),(24,44,29,49),(25,43,30,48),(31,154,36,159),(32,153,37,158),(33,152,38,157),(34,151,39,156),(35,160,40,155),(51,99,56,94),(52,98,57,93),(53,97,58,92),(54,96,59,91),(55,95,60,100),(61,104,66,109),(62,103,67,108),(63,102,68,107),(64,101,69,106),(65,110,70,105),(71,114,76,119),(72,113,77,118),(73,112,78,117),(74,111,79,116),(75,120,80,115),(81,122,86,127),(82,121,87,126),(83,130,88,125),(84,129,89,124),(85,128,90,123)]])
68 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5A | 5B | 8A | ··· | 8H | 10A | ··· | 10N | 10O | ··· | 10AD | 20A | ··· | 20H |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | 2 | 10 | ··· | 10 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D5 | D8 | SD16 | D10 | Dic5 | D10 | C5⋊D4 | C5⋊D4 | D4⋊D5 | D4.D5 |
| kernel | C2×D4⋊Dic5 | D4⋊Dic5 | C22×C5⋊2C8 | C2×C4⋊Dic5 | D4×C2×C10 | D4×C10 | C2×C20 | C22×C10 | C22×D4 | C2×C10 | C2×C10 | C22×C4 | C2×D4 | C2×D4 | C2×C4 | C23 | C22 | C22 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 3 | 1 | 2 | 4 | 4 | 2 | 8 | 4 | 12 | 4 | 4 | 4 |
Matrix representation of C2×D4⋊Dic5 ►in GL7(𝔽41)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 14 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 34 | 40 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 40 |
| 9 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 6 | 39 | 0 | 0 | 0 | 0 |
| 0 | 38 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 15 | 8 | 0 | 0 |
| 0 | 0 | 0 | 23 | 26 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 26 | 15 |
| 0 | 0 | 0 | 0 | 0 | 15 | 15 |
G:=sub<GL(7,GF(41))| [1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,1,0],[40,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,40,14,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0],[40,0,0,0,0,0,0,0,34,1,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,40],[9,0,0,0,0,0,0,0,6,38,0,0,0,0,0,39,35,0,0,0,0,0,0,0,15,23,0,0,0,0,0,8,26,0,0,0,0,0,0,0,26,15,0,0,0,0,0,15,15] >;
C2×D4⋊Dic5 in GAP, Magma, Sage, TeX
C_2\times D_4\rtimes {\rm Dic}_5 % in TeX
G:=Group("C2xD4:Dic5"); // GroupNames label
G:=SmallGroup(320,841);
// by ID
G=gap.SmallGroup(320,841);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,422,1684,438,102,12550]);
// 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=e*b*e^-1=b^-1,b*d=d*b,c*d=d*c,e*c*e^-1=b*c,e*d*e^-1=d^-1>;
// generators/relations