direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic5⋊D4, C24.59D10, (C2×D4)⋊38D10, Dic5⋊8(C2×D4), (C22×D4)⋊8D5, C10⋊5(C4⋊D4), (C2×Dic5)⋊22D4, (C22×C10)⋊12D4, C23⋊5(C5⋊D4), (D4×C10)⋊57C22, (C23×Dic5)⋊9C2, C22.148(D4×D5), (C2×C20).643C23, (C2×C10).297C24, C10.144(C22×D4), (C22×C4).271D10, C23.D5⋊63C22, D10⋊C4⋊72C22, C10.D4⋊74C22, (C23×C10).77C22, (C23×D5).76C22, C23.338(C22×D5), C22.310(C23×D5), C22.80(D4⋊2D5), (C22×C20).438C22, (C22×C10).231C23, (C2×Dic5).294C23, (C22×Dic5)⋊49C22, (C22×D5).128C23, C5⋊6(C2×C4⋊D4), (D4×C2×C10)⋊16C2, (C2×C10)⋊9(C2×D4), C2.104(C2×D4×D5), C22⋊1(C2×C5⋊D4), C10.106(C2×C4○D4), C2.70(C2×D4⋊2D5), (C2×C5⋊D4)⋊46C22, (C22×C5⋊D4)⋊15C2, (C2×C23.D5)⋊29C2, (C2×D10⋊C4)⋊42C2, C2.17(C22×C5⋊D4), (C2×C10.D4)⋊48C2, (C2×C4).237(C22×D5), (C2×C10).178(C4○D4), SmallGroup(320,1474)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Dic5⋊D4
G = < a,b,c,d,e | a2=b10=d4=e2=1, c2=b5, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, dcd-1=b5c, ce=ec, ede=d-1 >
Subgroups: 1486 in 426 conjugacy classes, 135 normal (31 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, C23, C23, C23, D5, C10, C10, C10, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C24, C24, Dic5, Dic5, C20, D10, C2×C10, C2×C10, C2×C10, C2×C22⋊C4, C2×C4⋊C4, C4⋊D4, C23×C4, C22×D4, C22×D4, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×D4, C22×D5, C22×D5, C22×C10, C22×C10, C22×C10, C2×C4⋊D4, C10.D4, D10⋊C4, C23.D5, C22×Dic5, C22×Dic5, C22×Dic5, C2×C5⋊D4, C2×C5⋊D4, C22×C20, D4×C10, D4×C10, C23×D5, C23×C10, C2×C10.D4, C2×D10⋊C4, Dic5⋊D4, C2×C23.D5, C23×Dic5, C22×C5⋊D4, D4×C2×C10, C2×Dic5⋊D4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C4○D4, C24, D10, C4⋊D4, C22×D4, C2×C4○D4, C5⋊D4, C22×D5, C2×C4⋊D4, D4×D5, D4⋊2D5, C2×C5⋊D4, C23×D5, Dic5⋊D4, C2×D4×D5, C2×D4⋊2D5, C22×C5⋊D4, C2×Dic5⋊D4
►On 160 points
Generators in S160
(1 107)(2 108)(3 109)(4 110)(5 101)(6 102)(7 103)(8 104)(9 105)(10 106)(11 72)(12 73)(13 74)(14 75)(15 76)(16 77)(17 78)(18 79)(19 80)(20 71)(21 98)(22 99)(23 100)(24 91)(25 92)(26 93)(27 94)(28 95)(29 96)(30 97)(31 124)(32 125)(33 126)(34 127)(35 128)(36 129)(37 130)(38 121)(39 122)(40 123)(41 118)(42 119)(43 120)(44 111)(45 112)(46 113)(47 114)(48 115)(49 116)(50 117)(51 144)(52 145)(53 146)(54 147)(55 148)(56 149)(57 150)(58 141)(59 142)(60 143)(61 138)(62 139)(63 140)(64 131)(65 132)(66 133)(67 134)(68 135)(69 136)(70 137)(81 158)(82 159)(83 160)(84 151)(85 152)(86 153)(87 154)(88 155)(89 156)(90 157)
(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 47 6 42)(2 46 7 41)(3 45 8 50)(4 44 9 49)(5 43 10 48)(11 131 16 136)(12 140 17 135)(13 139 18 134)(14 138 19 133)(15 137 20 132)(21 40 26 35)(22 39 27 34)(23 38 28 33)(24 37 29 32)(25 36 30 31)(51 90 56 85)(52 89 57 84)(53 88 58 83)(54 87 59 82)(55 86 60 81)(61 80 66 75)(62 79 67 74)(63 78 68 73)(64 77 69 72)(65 76 70 71)(91 130 96 125)(92 129 97 124)(93 128 98 123)(94 127 99 122)(95 126 100 121)(101 120 106 115)(102 119 107 114)(103 118 108 113)(104 117 109 112)(105 116 110 111)(141 160 146 155)(142 159 147 154)(143 158 148 153)(144 157 149 152)(145 156 150 151)
(1 87 27 74)(2 88 28 75)(3 89 29 76)(4 90 30 77)(5 81 21 78)(6 82 22 79)(7 83 23 80)(8 84 24 71)(9 85 25 72)(10 86 26 73)(11 105 152 92)(12 106 153 93)(13 107 154 94)(14 108 155 95)(15 109 156 96)(16 110 157 97)(17 101 158 98)(18 102 159 99)(19 103 160 100)(20 104 151 91)(31 64 44 51)(32 65 45 52)(33 66 46 53)(34 67 47 54)(35 68 48 55)(36 69 49 56)(37 70 50 57)(38 61 41 58)(39 62 42 59)(40 63 43 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 54)(2 55)(3 56)(4 57)(5 58)(6 59)(7 60)(8 51)(9 52)(10 53)(11 125)(12 126)(13 127)(14 128)(15 129)(16 130)(17 121)(18 122)(19 123)(20 124)(21 61)(22 62)(23 63)(24 64)(25 65)(26 66)(27 67)(28 68)(29 69)(30 70)(31 71)(32 72)(33 73)(34 74)(35 75)(36 76)(37 77)(38 78)(39 79)(40 80)(41 81)(42 82)(43 83)(44 84)(45 85)(46 86)(47 87)(48 88)(49 89)(50 90)(91 131)(92 132)(93 133)(94 134)(95 135)(96 136)(97 137)(98 138)(99 139)(100 140)(101 141)(102 142)(103 143)(104 144)(105 145)(106 146)(107 147)(108 148)(109 149)(110 150)(111 151)(112 152)(113 153)(114 154)(115 155)(116 156)(117 157)(118 158)(119 159)(120 160)
G:=sub<Sym(160)| (1,107)(2,108)(3,109)(4,110)(5,101)(6,102)(7,103)(8,104)(9,105)(10,106)(11,72)(12,73)(13,74)(14,75)(15,76)(16,77)(17,78)(18,79)(19,80)(20,71)(21,98)(22,99)(23,100)(24,91)(25,92)(26,93)(27,94)(28,95)(29,96)(30,97)(31,124)(32,125)(33,126)(34,127)(35,128)(36,129)(37,130)(38,121)(39,122)(40,123)(41,118)(42,119)(43,120)(44,111)(45,112)(46,113)(47,114)(48,115)(49,116)(50,117)(51,144)(52,145)(53,146)(54,147)(55,148)(56,149)(57,150)(58,141)(59,142)(60,143)(61,138)(62,139)(63,140)(64,131)(65,132)(66,133)(67,134)(68,135)(69,136)(70,137)(81,158)(82,159)(83,160)(84,151)(85,152)(86,153)(87,154)(88,155)(89,156)(90,157), (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), (1,47,6,42)(2,46,7,41)(3,45,8,50)(4,44,9,49)(5,43,10,48)(11,131,16,136)(12,140,17,135)(13,139,18,134)(14,138,19,133)(15,137,20,132)(21,40,26,35)(22,39,27,34)(23,38,28,33)(24,37,29,32)(25,36,30,31)(51,90,56,85)(52,89,57,84)(53,88,58,83)(54,87,59,82)(55,86,60,81)(61,80,66,75)(62,79,67,74)(63,78,68,73)(64,77,69,72)(65,76,70,71)(91,130,96,125)(92,129,97,124)(93,128,98,123)(94,127,99,122)(95,126,100,121)(101,120,106,115)(102,119,107,114)(103,118,108,113)(104,117,109,112)(105,116,110,111)(141,160,146,155)(142,159,147,154)(143,158,148,153)(144,157,149,152)(145,156,150,151), (1,87,27,74)(2,88,28,75)(3,89,29,76)(4,90,30,77)(5,81,21,78)(6,82,22,79)(7,83,23,80)(8,84,24,71)(9,85,25,72)(10,86,26,73)(11,105,152,92)(12,106,153,93)(13,107,154,94)(14,108,155,95)(15,109,156,96)(16,110,157,97)(17,101,158,98)(18,102,159,99)(19,103,160,100)(20,104,151,91)(31,64,44,51)(32,65,45,52)(33,66,46,53)(34,67,47,54)(35,68,48,55)(36,69,49,56)(37,70,50,57)(38,61,41,58)(39,62,42,59)(40,63,43,60)(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), (1,54)(2,55)(3,56)(4,57)(5,58)(6,59)(7,60)(8,51)(9,52)(10,53)(11,125)(12,126)(13,127)(14,128)(15,129)(16,130)(17,121)(18,122)(19,123)(20,124)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,81)(42,82)(43,83)(44,84)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(91,131)(92,132)(93,133)(94,134)(95,135)(96,136)(97,137)(98,138)(99,139)(100,140)(101,141)(102,142)(103,143)(104,144)(105,145)(106,146)(107,147)(108,148)(109,149)(110,150)(111,151)(112,152)(113,153)(114,154)(115,155)(116,156)(117,157)(118,158)(119,159)(120,160)>;
G:=Group( (1,107)(2,108)(3,109)(4,110)(5,101)(6,102)(7,103)(8,104)(9,105)(10,106)(11,72)(12,73)(13,74)(14,75)(15,76)(16,77)(17,78)(18,79)(19,80)(20,71)(21,98)(22,99)(23,100)(24,91)(25,92)(26,93)(27,94)(28,95)(29,96)(30,97)(31,124)(32,125)(33,126)(34,127)(35,128)(36,129)(37,130)(38,121)(39,122)(40,123)(41,118)(42,119)(43,120)(44,111)(45,112)(46,113)(47,114)(48,115)(49,116)(50,117)(51,144)(52,145)(53,146)(54,147)(55,148)(56,149)(57,150)(58,141)(59,142)(60,143)(61,138)(62,139)(63,140)(64,131)(65,132)(66,133)(67,134)(68,135)(69,136)(70,137)(81,158)(82,159)(83,160)(84,151)(85,152)(86,153)(87,154)(88,155)(89,156)(90,157), (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), (1,47,6,42)(2,46,7,41)(3,45,8,50)(4,44,9,49)(5,43,10,48)(11,131,16,136)(12,140,17,135)(13,139,18,134)(14,138,19,133)(15,137,20,132)(21,40,26,35)(22,39,27,34)(23,38,28,33)(24,37,29,32)(25,36,30,31)(51,90,56,85)(52,89,57,84)(53,88,58,83)(54,87,59,82)(55,86,60,81)(61,80,66,75)(62,79,67,74)(63,78,68,73)(64,77,69,72)(65,76,70,71)(91,130,96,125)(92,129,97,124)(93,128,98,123)(94,127,99,122)(95,126,100,121)(101,120,106,115)(102,119,107,114)(103,118,108,113)(104,117,109,112)(105,116,110,111)(141,160,146,155)(142,159,147,154)(143,158,148,153)(144,157,149,152)(145,156,150,151), (1,87,27,74)(2,88,28,75)(3,89,29,76)(4,90,30,77)(5,81,21,78)(6,82,22,79)(7,83,23,80)(8,84,24,71)(9,85,25,72)(10,86,26,73)(11,105,152,92)(12,106,153,93)(13,107,154,94)(14,108,155,95)(15,109,156,96)(16,110,157,97)(17,101,158,98)(18,102,159,99)(19,103,160,100)(20,104,151,91)(31,64,44,51)(32,65,45,52)(33,66,46,53)(34,67,47,54)(35,68,48,55)(36,69,49,56)(37,70,50,57)(38,61,41,58)(39,62,42,59)(40,63,43,60)(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), (1,54)(2,55)(3,56)(4,57)(5,58)(6,59)(7,60)(8,51)(9,52)(10,53)(11,125)(12,126)(13,127)(14,128)(15,129)(16,130)(17,121)(18,122)(19,123)(20,124)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,81)(42,82)(43,83)(44,84)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(91,131)(92,132)(93,133)(94,134)(95,135)(96,136)(97,137)(98,138)(99,139)(100,140)(101,141)(102,142)(103,143)(104,144)(105,145)(106,146)(107,147)(108,148)(109,149)(110,150)(111,151)(112,152)(113,153)(114,154)(115,155)(116,156)(117,157)(118,158)(119,159)(120,160) );
G=PermutationGroup([[(1,107),(2,108),(3,109),(4,110),(5,101),(6,102),(7,103),(8,104),(9,105),(10,106),(11,72),(12,73),(13,74),(14,75),(15,76),(16,77),(17,78),(18,79),(19,80),(20,71),(21,98),(22,99),(23,100),(24,91),(25,92),(26,93),(27,94),(28,95),(29,96),(30,97),(31,124),(32,125),(33,126),(34,127),(35,128),(36,129),(37,130),(38,121),(39,122),(40,123),(41,118),(42,119),(43,120),(44,111),(45,112),(46,113),(47,114),(48,115),(49,116),(50,117),(51,144),(52,145),(53,146),(54,147),(55,148),(56,149),(57,150),(58,141),(59,142),(60,143),(61,138),(62,139),(63,140),(64,131),(65,132),(66,133),(67,134),(68,135),(69,136),(70,137),(81,158),(82,159),(83,160),(84,151),(85,152),(86,153),(87,154),(88,155),(89,156),(90,157)], [(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)], [(1,47,6,42),(2,46,7,41),(3,45,8,50),(4,44,9,49),(5,43,10,48),(11,131,16,136),(12,140,17,135),(13,139,18,134),(14,138,19,133),(15,137,20,132),(21,40,26,35),(22,39,27,34),(23,38,28,33),(24,37,29,32),(25,36,30,31),(51,90,56,85),(52,89,57,84),(53,88,58,83),(54,87,59,82),(55,86,60,81),(61,80,66,75),(62,79,67,74),(63,78,68,73),(64,77,69,72),(65,76,70,71),(91,130,96,125),(92,129,97,124),(93,128,98,123),(94,127,99,122),(95,126,100,121),(101,120,106,115),(102,119,107,114),(103,118,108,113),(104,117,109,112),(105,116,110,111),(141,160,146,155),(142,159,147,154),(143,158,148,153),(144,157,149,152),(145,156,150,151)], [(1,87,27,74),(2,88,28,75),(3,89,29,76),(4,90,30,77),(5,81,21,78),(6,82,22,79),(7,83,23,80),(8,84,24,71),(9,85,25,72),(10,86,26,73),(11,105,152,92),(12,106,153,93),(13,107,154,94),(14,108,155,95),(15,109,156,96),(16,110,157,97),(17,101,158,98),(18,102,159,99),(19,103,160,100),(20,104,151,91),(31,64,44,51),(32,65,45,52),(33,66,46,53),(34,67,47,54),(35,68,48,55),(36,69,49,56),(37,70,50,57),(38,61,41,58),(39,62,42,59),(40,63,43,60),(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)], [(1,54),(2,55),(3,56),(4,57),(5,58),(6,59),(7,60),(8,51),(9,52),(10,53),(11,125),(12,126),(13,127),(14,128),(15,129),(16,130),(17,121),(18,122),(19,123),(20,124),(21,61),(22,62),(23,63),(24,64),(25,65),(26,66),(27,67),(28,68),(29,69),(30,70),(31,71),(32,72),(33,73),(34,74),(35,75),(36,76),(37,77),(38,78),(39,79),(40,80),(41,81),(42,82),(43,83),(44,84),(45,85),(46,86),(47,87),(48,88),(49,89),(50,90),(91,131),(92,132),(93,133),(94,134),(95,135),(96,136),(97,137),(98,138),(99,139),(100,140),(101,141),(102,142),(103,143),(104,144),(105,145),(106,146),(107,147),(108,148),(109,149),(110,150),(111,151),(112,152),(113,153),(114,154),(115,155),(116,156),(117,157),(118,158),(119,159),(120,160)]])
68 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 2N | 2O | 4A | 4B | 4C | ··· | 4J | 4K | 4L | 5A | 5B | 10A | ··· | 10N | 10O | ··· | 10AD | 20A | ··· | 20H |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 20 | 20 | 4 | 4 | 10 | ··· | 10 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D5 | C4○D4 | D10 | D10 | D10 | C5⋊D4 | D4×D5 | D4⋊2D5 |
| kernel | C2×Dic5⋊D4 | C2×C10.D4 | C2×D10⋊C4 | Dic5⋊D4 | C2×C23.D5 | C23×Dic5 | C22×C5⋊D4 | D4×C2×C10 | C2×Dic5 | C22×C10 | C22×D4 | C2×C10 | C22×C4 | C2×D4 | C24 | C23 | C22 | C22 |
| # reps | 1 | 1 | 1 | 8 | 1 | 1 | 2 | 1 | 4 | 4 | 2 | 4 | 2 | 8 | 4 | 16 | 4 | 4 |
Matrix representation of C2×Dic5⋊D4 ►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 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 40 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 40 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 38 | 38 | 0 | 0 | 0 | 0 |
| 17 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 38 | 38 | 0 | 0 |
| 0 | 0 | 17 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 17 | 1 | 0 | 0 | 0 | 0 |
| 40 | 24 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 1 | 0 | 0 |
| 0 | 0 | 40 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 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 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,40,0,0,0,0,1,7,0,0,0,0,0,0,0,40,0,0,0,0,1,7,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[38,17,0,0,0,0,38,3,0,0,0,0,0,0,38,17,0,0,0,0,38,3,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[17,40,0,0,0,0,1,24,0,0,0,0,0,0,17,40,0,0,0,0,1,24,0,0,0,0,0,0,0,40,0,0,0,0,1,0],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
C2×Dic5⋊D4 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_5\rtimes D_4 % in TeX
G:=Group("C2xDic5:D4"); // GroupNames label
G:=SmallGroup(320,1474);
// by ID
G=gap.SmallGroup(320,1474);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,758,675,297,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^10=d^4=e^2=1,c^2=b^5,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=b^-1,b*d=d*b,b*e=e*b,d*c*d^-1=b^5*c,c*e=e*c,e*d*e=d^-1>;
// generators/relations