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G = C2×Dic5⋊D4  order 320 = 26·5

Direct product of C2 and Dic5⋊D4

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×C10).297C24, (C2×C20).643C23, C10.144(C22×D4), (C22×C4).271D10, C23.D5⋊63C22, D10⋊C4⋊72C22, C10.D4⋊74C22, (C23×C10).77C22, (C23×D5).76C22, C22.310(C23×D5), C23.338(C22×D5), C22.80(D4⋊2D5), (C22×C10).231C23, (C22×C20).438C22, (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

Derived series
C1 — C2×C10 — C2×Dic5⋊D4
Chief series
C1 — C5 — C10 — C2×C10 — C22×D5 — C23×D5 — C22×C5⋊D4 — C2×Dic5⋊D4
Lower central
C5 — C2×C10 — C2×Dic5⋊D4

Subgroups: 1486 in 426 conjugacy classes, 135 normal (31 characteristic)
C1, C2 [×3], C2 [×4], C2 [×8], C4 [×10], C22, C22 [×10], C22 [×32], C5, C2×C4 [×2], C2×C4 [×24], D4 [×24], C23, C23 [×8], C23 [×18], D5 [×2], C10 [×3], C10 [×4], C10 [×6], C22⋊C4 [×8], C4⋊C4 [×4], C22×C4, C22×C4 [×11], C2×D4 [×4], C2×D4 [×20], C24 [×2], C24, Dic5 [×4], Dic5 [×4], C20 [×2], D10 [×10], C2×C10, C2×C10 [×10], C2×C10 [×22], C2×C22⋊C4 [×2], C2×C4⋊C4, C4⋊D4 [×8], C23×C4, C22×D4, C22×D4 [×2], C2×Dic5 [×10], C2×Dic5 [×12], C5⋊D4 [×16], C2×C20 [×2], C2×C20 [×2], C5×D4 [×8], C22×D5 [×2], C22×D5 [×6], C22×C10, C22×C10 [×8], C22×C10 [×10], C2×C4⋊D4, C10.D4 [×4], D10⋊C4 [×4], C23.D5 [×4], C22×Dic5 [×3], C22×Dic5 [×4], C22×Dic5 [×4], C2×C5⋊D4 [×8], C2×C5⋊D4 [×8], C22×C20, D4×C10 [×4], D4×C10 [×4], C23×D5, C23×C10 [×2], C2×C10.D4, C2×D10⋊C4, Dic5⋊D4 [×8], C2×C23.D5, C23×Dic5, C22×C5⋊D4 [×2], D4×C2×C10, C2×Dic5⋊D4

Quotients:
C1, C2 [×15], C22 [×35], D4 [×8], C23 [×15], D5, C2×D4 [×12], C4○D4 [×2], C24, D10 [×7], C4⋊D4 [×4], C22×D4 [×2], C2×C4○D4, C5⋊D4 [×4], C22×D5 [×7], C2×C4⋊D4, D4×D5 [×2], D4⋊2D5 [×2], C2×C5⋊D4 [×6], C23×D5, Dic5⋊D4 [×4], C2×D4×D5, C2×D4⋊2D5, C22×C5⋊D4, C2×Dic5⋊D4

Generators and relations
 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 >

Smallest permutation representation
►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 47 6 42)(2 46 7 41)(3 45 8 50)(4 44 9 49)(5 43 10 48)(11 133 16 138)(12 132 17 137)(13 131 18 136)(14 140 19 135)(15 139 20 134)(21 32 26 37)(22 31 27 36)(23 40 28 35)(24 39 29 34)(25 38 30 33)(51 82 56 87)(52 81 57 86)(53 90 58 85)(54 89 59 84)(55 88 60 83)(61 72 66 77)(62 71 67 76)(63 80 68 75)(64 79 69 74)(65 78 70 73)(91 122 96 127)(92 121 97 126)(93 130 98 125)(94 129 99 124)(95 128 100 123)(101 112 106 117)(102 111 107 116)(103 120 108 115)(104 119 109 114)(105 118 110 113)(141 152 146 157)(142 151 147 156)(143 160 148 155)(144 159 149 154)(145 158 150 153)

(1 87 27 76)(2 88 28 77)(3 89 29 78)(4 90 30 79)(5 81 21 80)(6 82 22 71)(7 83 23 72)(8 84 24 73)(9 85 25 74)(10 86 26 75)(11 105 154 94)(12 106 155 95)(13 107 156 96)(14 108 157 97)(15 109 158 98)(16 110 159 99)(17 101 160 100)(18 102 151 91)(19 103 152 92)(20 104 153 93)(31 62 42 51)(32 63 43 52)(33 64 44 53)(34 65 45 54)(35 66 46 55)(36 67 47 56)(37 68 48 57)(38 69 49 58)(39 70 50 59)(40 61 41 60)(111 142 122 131)(112 143 123 132)(113 144 124 133)(114 145 125 134)(115 146 126 135)(116 147 127 136)(117 148 128 137)(118 149 129 138)(119 150 130 139)(120 141 121 140)

(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), (1,47,6,42)(2,46,7,41)(3,45,8,50)(4,44,9,49)(5,43,10,48)(11,133,16,138)(12,132,17,137)(13,131,18,136)(14,140,19,135)(15,139,20,134)(21,32,26,37)(22,31,27,36)(23,40,28,35)(24,39,29,34)(25,38,30,33)(51,82,56,87)(52,81,57,86)(53,90,58,85)(54,89,59,84)(55,88,60,83)(61,72,66,77)(62,71,67,76)(63,80,68,75)(64,79,69,74)(65,78,70,73)(91,122,96,127)(92,121,97,126)(93,130,98,125)(94,129,99,124)(95,128,100,123)(101,112,106,117)(102,111,107,116)(103,120,108,115)(104,119,109,114)(105,118,110,113)(141,152,146,157)(142,151,147,156)(143,160,148,155)(144,159,149,154)(145,158,150,153), (1,87,27,76)(2,88,28,77)(3,89,29,78)(4,90,30,79)(5,81,21,80)(6,82,22,71)(7,83,23,72)(8,84,24,73)(9,85,25,74)(10,86,26,75)(11,105,154,94)(12,106,155,95)(13,107,156,96)(14,108,157,97)(15,109,158,98)(16,110,159,99)(17,101,160,100)(18,102,151,91)(19,103,152,92)(20,104,153,93)(31,62,42,51)(32,63,43,52)(33,64,44,53)(34,65,45,54)(35,66,46,55)(36,67,47,56)(37,68,48,57)(38,69,49,58)(39,70,50,59)(40,61,41,60)(111,142,122,131)(112,143,123,132)(113,144,124,133)(114,145,125,134)(115,146,126,135)(116,147,127,136)(117,148,128,137)(118,149,129,138)(119,150,130,139)(120,141,121,140), (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), (1,47,6,42)(2,46,7,41)(3,45,8,50)(4,44,9,49)(5,43,10,48)(11,133,16,138)(12,132,17,137)(13,131,18,136)(14,140,19,135)(15,139,20,134)(21,32,26,37)(22,31,27,36)(23,40,28,35)(24,39,29,34)(25,38,30,33)(51,82,56,87)(52,81,57,86)(53,90,58,85)(54,89,59,84)(55,88,60,83)(61,72,66,77)(62,71,67,76)(63,80,68,75)(64,79,69,74)(65,78,70,73)(91,122,96,127)(92,121,97,126)(93,130,98,125)(94,129,99,124)(95,128,100,123)(101,112,106,117)(102,111,107,116)(103,120,108,115)(104,119,109,114)(105,118,110,113)(141,152,146,157)(142,151,147,156)(143,160,148,155)(144,159,149,154)(145,158,150,153), (1,87,27,76)(2,88,28,77)(3,89,29,78)(4,90,30,79)(5,81,21,80)(6,82,22,71)(7,83,23,72)(8,84,24,73)(9,85,25,74)(10,86,26,75)(11,105,154,94)(12,106,155,95)(13,107,156,96)(14,108,157,97)(15,109,158,98)(16,110,159,99)(17,101,160,100)(18,102,151,91)(19,103,152,92)(20,104,153,93)(31,62,42,51)(32,63,43,52)(33,64,44,53)(34,65,45,54)(35,66,46,55)(36,67,47,56)(37,68,48,57)(38,69,49,58)(39,70,50,59)(40,61,41,60)(111,142,122,131)(112,143,123,132)(113,144,124,133)(114,145,125,134)(115,146,126,135)(116,147,127,136)(117,148,128,137)(118,149,129,138)(119,150,130,139)(120,141,121,140), (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)], [(1,47,6,42),(2,46,7,41),(3,45,8,50),(4,44,9,49),(5,43,10,48),(11,133,16,138),(12,132,17,137),(13,131,18,136),(14,140,19,135),(15,139,20,134),(21,32,26,37),(22,31,27,36),(23,40,28,35),(24,39,29,34),(25,38,30,33),(51,82,56,87),(52,81,57,86),(53,90,58,85),(54,89,59,84),(55,88,60,83),(61,72,66,77),(62,71,67,76),(63,80,68,75),(64,79,69,74),(65,78,70,73),(91,122,96,127),(92,121,97,126),(93,130,98,125),(94,129,99,124),(95,128,100,123),(101,112,106,117),(102,111,107,116),(103,120,108,115),(104,119,109,114),(105,118,110,113),(141,152,146,157),(142,151,147,156),(143,160,148,155),(144,159,149,154),(145,158,150,153)], [(1,87,27,76),(2,88,28,77),(3,89,29,78),(4,90,30,79),(5,81,21,80),(6,82,22,71),(7,83,23,72),(8,84,24,73),(9,85,25,74),(10,86,26,75),(11,105,154,94),(12,106,155,95),(13,107,156,96),(14,108,157,97),(15,109,158,98),(16,110,159,99),(17,101,160,100),(18,102,151,91),(19,103,152,92),(20,104,153,93),(31,62,42,51),(32,63,43,52),(33,64,44,53),(34,65,45,54),(35,66,46,55),(36,67,47,56),(37,68,48,57),(38,69,49,58),(39,70,50,59),(40,61,41,60),(111,142,122,131),(112,143,123,132),(113,144,124,133),(114,145,125,134),(115,146,126,135),(116,147,127,136),(117,148,128,137),(118,149,129,138),(119,150,130,139),(120,141,121,140)], [(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)])
 

Matrix representation ►G ⊆ GL6(𝔽41)

100000
010000
0040000
0004000
000010
000001
,
010000
4070000
000100
0040700
000010
000001
,
38380000
1730000
00383800
0017300
0000400
0000040
,
1710000
40240000
0017100
00402400
000001
0000400
,
4000000
0400000
001000
000100
000001
000010

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] >;
 

68 conjugacy classes

class 1 2A···2G2H2I2J2K2L2M2N2O4A4B4C···4J4K4L5A5B10A···10N10O···10AD20A···20H
order12···222222222444···4445510···1010···1020···20
size11···122224420204410···102020222···24···44···4

68 irreducible representations

dim111111112222222244
type+++++++++++++++-
imageC1C2C2C2C2C2C2C2D4D4D5C4○D4D10D10D10C5⋊D4D4×D5D4⋊2D5
kernelC2×Dic5⋊D4C2×C10.D4C2×D10⋊C4Dic5⋊D4C2×C23.D5C23×Dic5C22×C5⋊D4D4×C2×C10C2×Dic5C22×C10C22×D4C2×C10C22×C4C2×D4C24C23C22C22
# reps1118112144242841644

In GAP, Magma, Sage, TeX 

C_2\times 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
 

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