direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic5⋊4D4, C24.53D10, C10⋊3(C4×D4), C23⋊4(C4×D5), Dic5⋊9(C2×D4), C22⋊C4⋊50D10, (C2×Dic5)⋊23D4, D10⋊3(C22×C4), C10.29(C23×C4), (C2×C10).29C24, (C23×Dic5)⋊3C2, Dic5⋊2(C22×C4), C10.34(C22×D4), C22.124(D4×D5), (C2×C20).570C23, (C4×Dic5)⋊73C22, (C22×C4).312D10, D10⋊C4⋊56C22, C22.18(C23×D5), C10.D4⋊57C22, (C23×C10).55C22, C23.319(C22×D5), C22.66(D4⋊2D5), (C22×C20).351C22, (C22×C10).121C23, (C2×Dic5).370C23, (C22×Dic5)⋊41C22, (C23×D5).106C22, (C22×D5).159C23, C5⋊3(C2×C4×D4), C2.2(C2×D4×D5), C22⋊2(C2×C4×D5), C5⋊D4⋊9(C2×C4), (C2×C5⋊D4)⋊13C4, (C2×C4×Dic5)⋊30C2, (D5×C22×C4)⋊16C2, (C2×C4×D5)⋊64C22, C2.10(D5×C22×C4), (C2×C10)⋊6(C22×C4), (C2×C22⋊C4)⋊19D5, C10.67(C2×C4○D4), C2.2(C2×D4⋊2D5), (C10×C22⋊C4)⋊25C2, (C22×C10)⋊16(C2×C4), (C2×Dic5)⋊25(C2×C4), (C2×C10).380(C2×D4), (C22×D5)⋊15(C2×C4), (C2×D10⋊C4)⋊30C2, (C22×C5⋊D4).8C2, (C2×C10.D4)⋊35C2, (C5×C22⋊C4)⋊60C22, (C2×C4).256(C22×D5), (C2×C5⋊D4).95C22, (C2×C10).167(C4○D4), SmallGroup(320,1157)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Dic5⋊4D4
G = < a,b,c,d,e | a2=b10=d4=e2=1, c2=b5, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=dbd-1=b-1, be=eb, cd=dc, ce=ec, ede=d-1 >
Subgroups: 1358 in 426 conjugacy classes, 175 normal (31 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, C23, C23, C23, D5, C10, C10, C10, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C24, C24, Dic5, Dic5, C20, D10, D10, C2×C10, C2×C10, C2×C10, C2×C42, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C4×D4, C23×C4, C22×D4, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C22×D5, C22×D5, C22×C10, C22×C10, C22×C10, C2×C4×D4, C4×Dic5, C10.D4, D10⋊C4, C5×C22⋊C4, C2×C4×D5, C2×C4×D5, C22×Dic5, C22×Dic5, C22×Dic5, C2×C5⋊D4, C22×C20, C23×D5, C23×C10, Dic5⋊4D4, C2×C4×Dic5, C2×C10.D4, C2×D10⋊C4, C10×C22⋊C4, D5×C22×C4, C23×Dic5, C22×C5⋊D4, C2×Dic5⋊4D4
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D5, C22×C4, C2×D4, C4○D4, C24, D10, C4×D4, C23×C4, C22×D4, C2×C4○D4, C4×D5, C22×D5, C2×C4×D4, C2×C4×D5, D4×D5, D4⋊2D5, C23×D5, Dic5⋊4D4, D5×C22×C4, C2×D4×D5, C2×D4⋊2D5, C2×Dic5⋊4D4
►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 74)(12 75)(13 76)(14 77)(15 78)(16 79)(17 80)(18 71)(19 72)(20 73)(21 100)(22 91)(23 92)(24 93)(25 94)(26 95)(27 96)(28 97)(29 98)(30 99)(31 122)(32 123)(33 124)(34 125)(35 126)(36 127)(37 128)(38 129)(39 130)(40 121)(41 120)(42 111)(43 112)(44 113)(45 114)(46 115)(47 116)(48 117)(49 118)(50 119)(51 142)(52 143)(53 144)(54 145)(55 146)(56 147)(57 148)(58 149)(59 150)(60 141)(61 140)(62 131)(63 132)(64 133)(65 134)(66 135)(67 136)(68 137)(69 138)(70 139)(81 160)(82 151)(83 152)(84 153)(85 154)(86 155)(87 156)(88 157)(89 158)(90 159)
(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 42 6 47)(2 41 7 46)(3 50 8 45)(4 49 9 44)(5 48 10 43)(11 138 16 133)(12 137 17 132)(13 136 18 131)(14 135 19 140)(15 134 20 139)(21 37 26 32)(22 36 27 31)(23 35 28 40)(24 34 29 39)(25 33 30 38)(51 87 56 82)(52 86 57 81)(53 85 58 90)(54 84 59 89)(55 83 60 88)(61 77 66 72)(62 76 67 71)(63 75 68 80)(64 74 69 79)(65 73 70 78)(91 127 96 122)(92 126 97 121)(93 125 98 130)(94 124 99 129)(95 123 100 128)(101 117 106 112)(102 116 107 111)(103 115 108 120)(104 114 109 119)(105 113 110 118)(141 157 146 152)(142 156 147 151)(143 155 148 160)(144 154 149 159)(145 153 150 158)
(1 136 27 147)(2 135 28 146)(3 134 29 145)(4 133 30 144)(5 132 21 143)(6 131 22 142)(7 140 23 141)(8 139 24 150)(9 138 25 149)(10 137 26 148)(11 38 154 49)(12 37 155 48)(13 36 156 47)(14 35 157 46)(15 34 158 45)(16 33 159 44)(17 32 160 43)(18 31 151 42)(19 40 152 41)(20 39 153 50)(51 102 62 91)(52 101 63 100)(53 110 64 99)(54 109 65 98)(55 108 66 97)(56 107 67 96)(57 106 68 95)(58 105 69 94)(59 104 70 93)(60 103 61 92)(71 122 82 111)(72 121 83 120)(73 130 84 119)(74 129 85 118)(75 128 86 117)(76 127 87 116)(77 126 88 115)(78 125 89 114)(79 124 90 113)(80 123 81 112)
(1 56)(2 57)(3 58)(4 59)(5 60)(6 51)(7 52)(8 53)(9 54)(10 55)(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)(11,74)(12,75)(13,76)(14,77)(15,78)(16,79)(17,80)(18,71)(19,72)(20,73)(21,100)(22,91)(23,92)(24,93)(25,94)(26,95)(27,96)(28,97)(29,98)(30,99)(31,122)(32,123)(33,124)(34,125)(35,126)(36,127)(37,128)(38,129)(39,130)(40,121)(41,120)(42,111)(43,112)(44,113)(45,114)(46,115)(47,116)(48,117)(49,118)(50,119)(51,142)(52,143)(53,144)(54,145)(55,146)(56,147)(57,148)(58,149)(59,150)(60,141)(61,140)(62,131)(63,132)(64,133)(65,134)(66,135)(67,136)(68,137)(69,138)(70,139)(81,160)(82,151)(83,152)(84,153)(85,154)(86,155)(87,156)(88,157)(89,158)(90,159), (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), (1,42,6,47)(2,41,7,46)(3,50,8,45)(4,49,9,44)(5,48,10,43)(11,138,16,133)(12,137,17,132)(13,136,18,131)(14,135,19,140)(15,134,20,139)(21,37,26,32)(22,36,27,31)(23,35,28,40)(24,34,29,39)(25,33,30,38)(51,87,56,82)(52,86,57,81)(53,85,58,90)(54,84,59,89)(55,83,60,88)(61,77,66,72)(62,76,67,71)(63,75,68,80)(64,74,69,79)(65,73,70,78)(91,127,96,122)(92,126,97,121)(93,125,98,130)(94,124,99,129)(95,123,100,128)(101,117,106,112)(102,116,107,111)(103,115,108,120)(104,114,109,119)(105,113,110,118)(141,157,146,152)(142,156,147,151)(143,155,148,160)(144,154,149,159)(145,153,150,158), (1,136,27,147)(2,135,28,146)(3,134,29,145)(4,133,30,144)(5,132,21,143)(6,131,22,142)(7,140,23,141)(8,139,24,150)(9,138,25,149)(10,137,26,148)(11,38,154,49)(12,37,155,48)(13,36,156,47)(14,35,157,46)(15,34,158,45)(16,33,159,44)(17,32,160,43)(18,31,151,42)(19,40,152,41)(20,39,153,50)(51,102,62,91)(52,101,63,100)(53,110,64,99)(54,109,65,98)(55,108,66,97)(56,107,67,96)(57,106,68,95)(58,105,69,94)(59,104,70,93)(60,103,61,92)(71,122,82,111)(72,121,83,120)(73,130,84,119)(74,129,85,118)(75,128,86,117)(76,127,87,116)(77,126,88,115)(78,125,89,114)(79,124,90,113)(80,123,81,112), (1,56)(2,57)(3,58)(4,59)(5,60)(6,51)(7,52)(8,53)(9,54)(10,55)(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)(11,74)(12,75)(13,76)(14,77)(15,78)(16,79)(17,80)(18,71)(19,72)(20,73)(21,100)(22,91)(23,92)(24,93)(25,94)(26,95)(27,96)(28,97)(29,98)(30,99)(31,122)(32,123)(33,124)(34,125)(35,126)(36,127)(37,128)(38,129)(39,130)(40,121)(41,120)(42,111)(43,112)(44,113)(45,114)(46,115)(47,116)(48,117)(49,118)(50,119)(51,142)(52,143)(53,144)(54,145)(55,146)(56,147)(57,148)(58,149)(59,150)(60,141)(61,140)(62,131)(63,132)(64,133)(65,134)(66,135)(67,136)(68,137)(69,138)(70,139)(81,160)(82,151)(83,152)(84,153)(85,154)(86,155)(87,156)(88,157)(89,158)(90,159), (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), (1,42,6,47)(2,41,7,46)(3,50,8,45)(4,49,9,44)(5,48,10,43)(11,138,16,133)(12,137,17,132)(13,136,18,131)(14,135,19,140)(15,134,20,139)(21,37,26,32)(22,36,27,31)(23,35,28,40)(24,34,29,39)(25,33,30,38)(51,87,56,82)(52,86,57,81)(53,85,58,90)(54,84,59,89)(55,83,60,88)(61,77,66,72)(62,76,67,71)(63,75,68,80)(64,74,69,79)(65,73,70,78)(91,127,96,122)(92,126,97,121)(93,125,98,130)(94,124,99,129)(95,123,100,128)(101,117,106,112)(102,116,107,111)(103,115,108,120)(104,114,109,119)(105,113,110,118)(141,157,146,152)(142,156,147,151)(143,155,148,160)(144,154,149,159)(145,153,150,158), (1,136,27,147)(2,135,28,146)(3,134,29,145)(4,133,30,144)(5,132,21,143)(6,131,22,142)(7,140,23,141)(8,139,24,150)(9,138,25,149)(10,137,26,148)(11,38,154,49)(12,37,155,48)(13,36,156,47)(14,35,157,46)(15,34,158,45)(16,33,159,44)(17,32,160,43)(18,31,151,42)(19,40,152,41)(20,39,153,50)(51,102,62,91)(52,101,63,100)(53,110,64,99)(54,109,65,98)(55,108,66,97)(56,107,67,96)(57,106,68,95)(58,105,69,94)(59,104,70,93)(60,103,61,92)(71,122,82,111)(72,121,83,120)(73,130,84,119)(74,129,85,118)(75,128,86,117)(76,127,87,116)(77,126,88,115)(78,125,89,114)(79,124,90,113)(80,123,81,112), (1,56)(2,57)(3,58)(4,59)(5,60)(6,51)(7,52)(8,53)(9,54)(10,55)(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),(11,74),(12,75),(13,76),(14,77),(15,78),(16,79),(17,80),(18,71),(19,72),(20,73),(21,100),(22,91),(23,92),(24,93),(25,94),(26,95),(27,96),(28,97),(29,98),(30,99),(31,122),(32,123),(33,124),(34,125),(35,126),(36,127),(37,128),(38,129),(39,130),(40,121),(41,120),(42,111),(43,112),(44,113),(45,114),(46,115),(47,116),(48,117),(49,118),(50,119),(51,142),(52,143),(53,144),(54,145),(55,146),(56,147),(57,148),(58,149),(59,150),(60,141),(61,140),(62,131),(63,132),(64,133),(65,134),(66,135),(67,136),(68,137),(69,138),(70,139),(81,160),(82,151),(83,152),(84,153),(85,154),(86,155),(87,156),(88,157),(89,158),(90,159)], [(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)], [(1,42,6,47),(2,41,7,46),(3,50,8,45),(4,49,9,44),(5,48,10,43),(11,138,16,133),(12,137,17,132),(13,136,18,131),(14,135,19,140),(15,134,20,139),(21,37,26,32),(22,36,27,31),(23,35,28,40),(24,34,29,39),(25,33,30,38),(51,87,56,82),(52,86,57,81),(53,85,58,90),(54,84,59,89),(55,83,60,88),(61,77,66,72),(62,76,67,71),(63,75,68,80),(64,74,69,79),(65,73,70,78),(91,127,96,122),(92,126,97,121),(93,125,98,130),(94,124,99,129),(95,123,100,128),(101,117,106,112),(102,116,107,111),(103,115,108,120),(104,114,109,119),(105,113,110,118),(141,157,146,152),(142,156,147,151),(143,155,148,160),(144,154,149,159),(145,153,150,158)], [(1,136,27,147),(2,135,28,146),(3,134,29,145),(4,133,30,144),(5,132,21,143),(6,131,22,142),(7,140,23,141),(8,139,24,150),(9,138,25,149),(10,137,26,148),(11,38,154,49),(12,37,155,48),(13,36,156,47),(14,35,157,46),(15,34,158,45),(16,33,159,44),(17,32,160,43),(18,31,151,42),(19,40,152,41),(20,39,153,50),(51,102,62,91),(52,101,63,100),(53,110,64,99),(54,109,65,98),(55,108,66,97),(56,107,67,96),(57,106,68,95),(58,105,69,94),(59,104,70,93),(60,103,61,92),(71,122,82,111),(72,121,83,120),(73,130,84,119),(74,129,85,118),(75,128,86,117),(76,127,87,116),(77,126,88,115),(78,125,89,114),(79,124,90,113),(80,123,81,112)], [(1,56),(2,57),(3,58),(4,59),(5,60),(6,51),(7,52),(8,53),(9,54),(10,55),(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)]])
80 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 2N | 2O | 4A | ··· | 4H | 4I | ··· | 4P | 4Q | ··· | 4X | 5A | 5B | 10A | ··· | 10N | 10O | ··· | 10V | 20A | ··· | 20P |
| 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 | 10 | 10 | 10 | 10 | 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 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D5 | C4○D4 | D10 | D10 | D10 | C4×D5 | D4×D5 | D4⋊2D5 |
| kernel | C2×Dic5⋊4D4 | Dic5⋊4D4 | C2×C4×Dic5 | C2×C10.D4 | C2×D10⋊C4 | C10×C22⋊C4 | D5×C22×C4 | C23×Dic5 | C22×C5⋊D4 | C2×C5⋊D4 | C2×Dic5 | C2×C22⋊C4 | C2×C10 | C22⋊C4 | C22×C4 | C24 | C23 | C22 | C22 |
| # reps | 1 | 8 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 16 | 4 | 2 | 4 | 8 | 4 | 2 | 16 | 4 | 4 |
Matrix representation of C2×Dic5⋊4D4 ►in GL6(𝔽41)
| 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 | 0 | 1 |
| 7 | 40 | 0 | 0 | 0 | 0 |
| 8 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 1 | 0 | 0 |
| 0 | 0 | 33 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 34 | 1 | 0 | 0 | 0 | 0 |
| 34 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 32 | 0 | 0 |
| 0 | 0 | 22 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 7 | 40 | 0 | 0 | 0 | 0 |
| 7 | 34 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 1 | 0 | 0 |
| 0 | 0 | 34 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 39 |
| 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 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 | 0 | 40 | 39 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[7,8,0,0,0,0,40,40,0,0,0,0,0,0,34,33,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[34,34,0,0,0,0,1,7,0,0,0,0,0,0,22,22,0,0,0,0,32,19,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[7,7,0,0,0,0,40,34,0,0,0,0,0,0,34,34,0,0,0,0,1,7,0,0,0,0,0,0,40,1,0,0,0,0,39,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,39,1] >;
C2×Dic5⋊4D4 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_5\rtimes_4D_4 % in TeX
G:=Group("C2xDic5:4D4"); // GroupNames label
G:=SmallGroup(320,1157);
// by ID
G=gap.SmallGroup(320,1157);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,758,297,80,12550]);
// 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=d*b*d^-1=b^-1,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e=d^-1>;
// generators/relations