metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4○D4⋊1Dic5, Q8⋊4(C2×Dic5), D4⋊4(C2×Dic5), (C2×C20).476D4, C20.212(C2×D4), (C2×D4).201D10, Q8⋊Dic5⋊40C2, D4⋊Dic5⋊40C2, (C2×Q8).170D10, C2.5(D4⋊D10), C20.142(C22×C4), (C2×C20).479C23, (C22×C4).161D10, (C22×C10).111D4, C23.65(C5⋊D4), C5⋊6(C23.36D4), C4.22(C23.D5), C4.13(C22×Dic5), C10.124(C8⋊C22), C20.137(C22⋊C4), C2.5(D4.9D10), (D4×C10).242C22, C4⋊Dic5.354C22, (Q8×C10).205C22, C22.2(C23.D5), C10.124(C8.C22), (C22×C20).205C22, (C5×C4○D4)⋊7C4, (C5×D4)⋊27(C2×C4), (C5×Q8)⋊25(C2×C4), (C2×C4○D4).1D5, C4.94(C2×C5⋊D4), (C2×C4⋊Dic5)⋊36C2, (C10×C4○D4).1C2, (C2×C20).295(C2×C4), (C2×C10).565(C2×D4), (C2×C4.Dic5)⋊19C2, (C2×C4).28(C2×Dic5), C22.96(C2×C5⋊D4), C2.17(C2×C23.D5), (C2×C4).261(C5⋊D4), C10.122(C2×C22⋊C4), (C2×C4).564(C22×D5), (C2×C10).88(C22⋊C4), (C2×C5⋊2C8).177C22, SmallGroup(320,859)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4○D4⋊Dic5
G = < a,b,c,d,e | a4=c2=d10=1, b2=a2, e2=d5, ab=ba, ac=ca, ad=da, eae-1=a-1, cbc=a2b, bd=db, ebe-1=abc, cd=dc, ce=ec, ede-1=d-1 >
Subgroups: 446 in 162 conjugacy classes, 71 normal (31 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C22, C5, C8, C2×C4, C2×C4, C2×C4, D4, D4, Q8, Q8, C23, C23, C10, C10, C4⋊C4, C2×C8, M4(2), C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, C4○D4, Dic5, C20, C20, C20, C2×C10, C2×C10, C2×C10, D4⋊C4, Q8⋊C4, C2×C4⋊C4, C2×M4(2), C2×C4○D4, C5⋊2C8, C2×Dic5, C2×C20, C2×C20, C2×C20, C5×D4, C5×D4, C5×Q8, C5×Q8, C22×C10, C22×C10, C23.36D4, C2×C5⋊2C8, C4.Dic5, C4⋊Dic5, C4⋊Dic5, C22×Dic5, C22×C20, C22×C20, D4×C10, D4×C10, Q8×C10, C5×C4○D4, C5×C4○D4, D4⋊Dic5, Q8⋊Dic5, C2×C4.Dic5, C2×C4⋊Dic5, C10×C4○D4, C4○D4⋊Dic5
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D5, C22⋊C4, C22×C4, C2×D4, Dic5, D10, C2×C22⋊C4, C8⋊C22, C8.C22, C2×Dic5, C5⋊D4, C22×D5, C23.36D4, C23.D5, C22×Dic5, C2×C5⋊D4, D4⋊D10, D4.9D10, C2×C23.D5, C4○D4⋊Dic5
►On 160 points
Generators in S160
(1 85 39 70)(2 86 40 61)(3 87 31 62)(4 88 32 63)(5 89 33 64)(6 90 34 65)(7 81 35 66)(8 82 36 67)(9 83 37 68)(10 84 38 69)(11 57 47 78)(12 58 48 79)(13 59 49 80)(14 60 50 71)(15 51 41 72)(16 52 42 73)(17 53 43 74)(18 54 44 75)(19 55 45 76)(20 56 46 77)(21 106 135 116)(22 107 136 117)(23 108 137 118)(24 109 138 119)(25 110 139 120)(26 101 140 111)(27 102 131 112)(28 103 132 113)(29 104 133 114)(30 105 134 115)(91 152 128 142)(92 153 129 143)(93 154 130 144)(94 155 121 145)(95 156 122 146)(96 157 123 147)(97 158 124 148)(98 159 125 149)(99 160 126 150)(100 151 127 141)
(1 79 39 58)(2 80 40 59)(3 71 31 60)(4 72 32 51)(5 73 33 52)(6 74 34 53)(7 75 35 54)(8 76 36 55)(9 77 37 56)(10 78 38 57)(11 69 47 84)(12 70 48 85)(13 61 49 86)(14 62 50 87)(15 63 41 88)(16 64 42 89)(17 65 43 90)(18 66 44 81)(19 67 45 82)(20 68 46 83)(21 106 135 116)(22 107 136 117)(23 108 137 118)(24 109 138 119)(25 110 139 120)(26 101 140 111)(27 102 131 112)(28 103 132 113)(29 104 133 114)(30 105 134 115)(91 142 128 152)(92 143 129 153)(93 144 130 154)(94 145 121 155)(95 146 122 156)(96 147 123 157)(97 148 124 158)(98 149 125 159)(99 150 126 160)(100 141 127 151)
(1 58)(2 59)(3 60)(4 51)(5 52)(6 53)(7 54)(8 55)(9 56)(10 57)(11 69)(12 70)(13 61)(14 62)(15 63)(16 64)(17 65)(18 66)(19 67)(20 68)(21 122)(22 123)(23 124)(24 125)(25 126)(26 127)(27 128)(28 129)(29 130)(30 121)(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)(91 131)(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)
(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)
(1 106 6 101)(2 105 7 110)(3 104 8 109)(4 103 9 108)(5 102 10 107)(11 96 16 91)(12 95 17 100)(13 94 18 99)(14 93 19 98)(15 92 20 97)(21 90 26 85)(22 89 27 84)(23 88 28 83)(24 87 29 82)(25 86 30 81)(31 114 36 119)(32 113 37 118)(33 112 38 117)(34 111 39 116)(35 120 40 115)(41 129 46 124)(42 128 47 123)(43 127 48 122)(44 126 49 121)(45 125 50 130)(51 143 56 148)(52 142 57 147)(53 141 58 146)(54 150 59 145)(55 149 60 144)(61 134 66 139)(62 133 67 138)(63 132 68 137)(64 131 69 136)(65 140 70 135)(71 154 76 159)(72 153 77 158)(73 152 78 157)(74 151 79 156)(75 160 80 155)
G:=sub<Sym(160)| (1,85,39,70)(2,86,40,61)(3,87,31,62)(4,88,32,63)(5,89,33,64)(6,90,34,65)(7,81,35,66)(8,82,36,67)(9,83,37,68)(10,84,38,69)(11,57,47,78)(12,58,48,79)(13,59,49,80)(14,60,50,71)(15,51,41,72)(16,52,42,73)(17,53,43,74)(18,54,44,75)(19,55,45,76)(20,56,46,77)(21,106,135,116)(22,107,136,117)(23,108,137,118)(24,109,138,119)(25,110,139,120)(26,101,140,111)(27,102,131,112)(28,103,132,113)(29,104,133,114)(30,105,134,115)(91,152,128,142)(92,153,129,143)(93,154,130,144)(94,155,121,145)(95,156,122,146)(96,157,123,147)(97,158,124,148)(98,159,125,149)(99,160,126,150)(100,151,127,141), (1,79,39,58)(2,80,40,59)(3,71,31,60)(4,72,32,51)(5,73,33,52)(6,74,34,53)(7,75,35,54)(8,76,36,55)(9,77,37,56)(10,78,38,57)(11,69,47,84)(12,70,48,85)(13,61,49,86)(14,62,50,87)(15,63,41,88)(16,64,42,89)(17,65,43,90)(18,66,44,81)(19,67,45,82)(20,68,46,83)(21,106,135,116)(22,107,136,117)(23,108,137,118)(24,109,138,119)(25,110,139,120)(26,101,140,111)(27,102,131,112)(28,103,132,113)(29,104,133,114)(30,105,134,115)(91,142,128,152)(92,143,129,153)(93,144,130,154)(94,145,121,155)(95,146,122,156)(96,147,123,157)(97,148,124,158)(98,149,125,159)(99,150,126,160)(100,141,127,151), (1,58)(2,59)(3,60)(4,51)(5,52)(6,53)(7,54)(8,55)(9,56)(10,57)(11,69)(12,70)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,122)(22,123)(23,124)(24,125)(25,126)(26,127)(27,128)(28,129)(29,130)(30,121)(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)(91,131)(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), (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), (1,106,6,101)(2,105,7,110)(3,104,8,109)(4,103,9,108)(5,102,10,107)(11,96,16,91)(12,95,17,100)(13,94,18,99)(14,93,19,98)(15,92,20,97)(21,90,26,85)(22,89,27,84)(23,88,28,83)(24,87,29,82)(25,86,30,81)(31,114,36,119)(32,113,37,118)(33,112,38,117)(34,111,39,116)(35,120,40,115)(41,129,46,124)(42,128,47,123)(43,127,48,122)(44,126,49,121)(45,125,50,130)(51,143,56,148)(52,142,57,147)(53,141,58,146)(54,150,59,145)(55,149,60,144)(61,134,66,139)(62,133,67,138)(63,132,68,137)(64,131,69,136)(65,140,70,135)(71,154,76,159)(72,153,77,158)(73,152,78,157)(74,151,79,156)(75,160,80,155)>;
G:=Group( (1,85,39,70)(2,86,40,61)(3,87,31,62)(4,88,32,63)(5,89,33,64)(6,90,34,65)(7,81,35,66)(8,82,36,67)(9,83,37,68)(10,84,38,69)(11,57,47,78)(12,58,48,79)(13,59,49,80)(14,60,50,71)(15,51,41,72)(16,52,42,73)(17,53,43,74)(18,54,44,75)(19,55,45,76)(20,56,46,77)(21,106,135,116)(22,107,136,117)(23,108,137,118)(24,109,138,119)(25,110,139,120)(26,101,140,111)(27,102,131,112)(28,103,132,113)(29,104,133,114)(30,105,134,115)(91,152,128,142)(92,153,129,143)(93,154,130,144)(94,155,121,145)(95,156,122,146)(96,157,123,147)(97,158,124,148)(98,159,125,149)(99,160,126,150)(100,151,127,141), (1,79,39,58)(2,80,40,59)(3,71,31,60)(4,72,32,51)(5,73,33,52)(6,74,34,53)(7,75,35,54)(8,76,36,55)(9,77,37,56)(10,78,38,57)(11,69,47,84)(12,70,48,85)(13,61,49,86)(14,62,50,87)(15,63,41,88)(16,64,42,89)(17,65,43,90)(18,66,44,81)(19,67,45,82)(20,68,46,83)(21,106,135,116)(22,107,136,117)(23,108,137,118)(24,109,138,119)(25,110,139,120)(26,101,140,111)(27,102,131,112)(28,103,132,113)(29,104,133,114)(30,105,134,115)(91,142,128,152)(92,143,129,153)(93,144,130,154)(94,145,121,155)(95,146,122,156)(96,147,123,157)(97,148,124,158)(98,149,125,159)(99,150,126,160)(100,141,127,151), (1,58)(2,59)(3,60)(4,51)(5,52)(6,53)(7,54)(8,55)(9,56)(10,57)(11,69)(12,70)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,122)(22,123)(23,124)(24,125)(25,126)(26,127)(27,128)(28,129)(29,130)(30,121)(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)(91,131)(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), (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), (1,106,6,101)(2,105,7,110)(3,104,8,109)(4,103,9,108)(5,102,10,107)(11,96,16,91)(12,95,17,100)(13,94,18,99)(14,93,19,98)(15,92,20,97)(21,90,26,85)(22,89,27,84)(23,88,28,83)(24,87,29,82)(25,86,30,81)(31,114,36,119)(32,113,37,118)(33,112,38,117)(34,111,39,116)(35,120,40,115)(41,129,46,124)(42,128,47,123)(43,127,48,122)(44,126,49,121)(45,125,50,130)(51,143,56,148)(52,142,57,147)(53,141,58,146)(54,150,59,145)(55,149,60,144)(61,134,66,139)(62,133,67,138)(63,132,68,137)(64,131,69,136)(65,140,70,135)(71,154,76,159)(72,153,77,158)(73,152,78,157)(74,151,79,156)(75,160,80,155) );
G=PermutationGroup([[(1,85,39,70),(2,86,40,61),(3,87,31,62),(4,88,32,63),(5,89,33,64),(6,90,34,65),(7,81,35,66),(8,82,36,67),(9,83,37,68),(10,84,38,69),(11,57,47,78),(12,58,48,79),(13,59,49,80),(14,60,50,71),(15,51,41,72),(16,52,42,73),(17,53,43,74),(18,54,44,75),(19,55,45,76),(20,56,46,77),(21,106,135,116),(22,107,136,117),(23,108,137,118),(24,109,138,119),(25,110,139,120),(26,101,140,111),(27,102,131,112),(28,103,132,113),(29,104,133,114),(30,105,134,115),(91,152,128,142),(92,153,129,143),(93,154,130,144),(94,155,121,145),(95,156,122,146),(96,157,123,147),(97,158,124,148),(98,159,125,149),(99,160,126,150),(100,151,127,141)], [(1,79,39,58),(2,80,40,59),(3,71,31,60),(4,72,32,51),(5,73,33,52),(6,74,34,53),(7,75,35,54),(8,76,36,55),(9,77,37,56),(10,78,38,57),(11,69,47,84),(12,70,48,85),(13,61,49,86),(14,62,50,87),(15,63,41,88),(16,64,42,89),(17,65,43,90),(18,66,44,81),(19,67,45,82),(20,68,46,83),(21,106,135,116),(22,107,136,117),(23,108,137,118),(24,109,138,119),(25,110,139,120),(26,101,140,111),(27,102,131,112),(28,103,132,113),(29,104,133,114),(30,105,134,115),(91,142,128,152),(92,143,129,153),(93,144,130,154),(94,145,121,155),(95,146,122,156),(96,147,123,157),(97,148,124,158),(98,149,125,159),(99,150,126,160),(100,141,127,151)], [(1,58),(2,59),(3,60),(4,51),(5,52),(6,53),(7,54),(8,55),(9,56),(10,57),(11,69),(12,70),(13,61),(14,62),(15,63),(16,64),(17,65),(18,66),(19,67),(20,68),(21,122),(22,123),(23,124),(24,125),(25,126),(26,127),(27,128),(28,129),(29,130),(30,121),(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),(91,131),(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)], [(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)], [(1,106,6,101),(2,105,7,110),(3,104,8,109),(4,103,9,108),(5,102,10,107),(11,96,16,91),(12,95,17,100),(13,94,18,99),(14,93,19,98),(15,92,20,97),(21,90,26,85),(22,89,27,84),(23,88,28,83),(24,87,29,82),(25,86,30,81),(31,114,36,119),(32,113,37,118),(33,112,38,117),(34,111,39,116),(35,120,40,115),(41,129,46,124),(42,128,47,123),(43,127,48,122),(44,126,49,121),(45,125,50,130),(51,143,56,148),(52,142,57,147),(53,141,58,146),(54,150,59,145),(55,149,60,144),(61,134,66,139),(62,133,67,138),(63,132,68,137),(64,131,69,136),(65,140,70,135),(71,154,76,159),(72,153,77,158),(73,152,78,157),(74,151,79,156),(75,160,80,155)]])
62 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 10G | ··· | 10R | 20A | ··· | 20H | 20I | ··· | 20T |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 10 | ··· | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | 4 | 20 | 20 | 20 | 20 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
62 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 | D4 | D4 | D5 | D10 | D10 | D10 | Dic5 | C5⋊D4 | C5⋊D4 | C8⋊C22 | C8.C22 | D4⋊D10 | D4.9D10 |
| kernel | C4○D4⋊Dic5 | D4⋊Dic5 | Q8⋊Dic5 | C2×C4.Dic5 | C2×C4⋊Dic5 | C10×C4○D4 | C5×C4○D4 | C2×C20 | C22×C10 | C2×C4○D4 | C22×C4 | C2×D4 | C2×Q8 | C4○D4 | C2×C4 | C23 | C10 | C10 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 8 | 3 | 1 | 2 | 2 | 2 | 2 | 8 | 12 | 4 | 1 | 1 | 4 | 4 |
Matrix representation of C4○D4⋊Dic5 ►in GL6(𝔽41)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 33 | 32 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 0 | 33 | 32 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 32 | 0 |
| 0 | 0 | 0 | 0 | 8 | 9 |
| 0 | 0 | 32 | 0 | 0 | 0 |
| 0 | 0 | 8 | 9 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 32 | 0 |
| 0 | 0 | 0 | 0 | 8 | 9 |
| 0 | 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 33 | 32 | 0 | 0 |
| 23 | 0 | 0 | 0 | 0 | 0 |
| 0 | 25 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 0 | 0 | 0 |
| 0 | 0 | 31 | 23 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 0 |
| 0 | 0 | 0 | 0 | 31 | 23 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 29 | 14 | 12 | 27 |
| 0 | 0 | 38 | 12 | 3 | 29 |
| 0 | 0 | 12 | 27 | 12 | 27 |
| 0 | 0 | 3 | 29 | 3 | 29 |
G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,9,33,0,0,0,0,0,32,0,0,0,0,0,0,9,33,0,0,0,0,0,32],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,32,8,0,0,0,0,0,9,0,0,32,8,0,0,0,0,0,9,0,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,9,33,0,0,0,0,0,32,0,0,32,8,0,0,0,0,0,9,0,0],[23,0,0,0,0,0,0,25,0,0,0,0,0,0,25,31,0,0,0,0,0,23,0,0,0,0,0,0,25,31,0,0,0,0,0,23],[0,1,0,0,0,0,40,0,0,0,0,0,0,0,29,38,12,3,0,0,14,12,27,29,0,0,12,3,12,3,0,0,27,29,27,29] >;
C4○D4⋊Dic5 in GAP, Magma, Sage, TeX
C_4\circ D_4\rtimes {\rm Dic}_5 % in TeX
G:=Group("C4oD4:Dic5"); // GroupNames label
G:=SmallGroup(320,859);
// by ID
G=gap.SmallGroup(320,859);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,422,387,1684,438,102,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=c^2=d^10=1,b^2=a^2,e^2=d^5,a*b=b*a,a*c=c*a,a*d=d*a,e*a*e^-1=a^-1,c*b*c=a^2*b,b*d=d*b,e*b*e^-1=a*b*c,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations