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G = C2×Dic5⋊D4order 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, Dic58(C2×D4), (C22×D4)⋊8D5, C105(C4⋊D4), (C2×Dic5)⋊22D4, (C22×C10)⋊12D4, C235(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.D563C22, D10⋊C472C22, C10.D474C22, (C23×C10).77C22, (C23×D5).76C22, C23.338(C22×D5), C22.310(C23×D5), C22.80(D42D5), (C22×C20).438C22, (C22×C10).231C23, (C2×Dic5).294C23, (C22×Dic5)⋊49C22, (C22×D5).128C23, C56(C2×C4⋊D4), (D4×C2×C10)⋊16C2, (C2×C10)⋊9(C2×D4), C2.104(C2×D4×D5), C221(C2×C5⋊D4), C10.106(C2×C4○D4), C2.70(C2×D42D5), (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

C1C2×C10 — C2×Dic5⋊D4
C1C5C10C2×C10C22×D5C23×D5C22×C5⋊D4 — C2×Dic5⋊D4
C5C2×C10 — C2×Dic5⋊D4
C1C23C22×D4

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 [×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], D42D5 [×2], C2×C5⋊D4 [×6], C23×D5, Dic5⋊D4 [×4], C2×D4×D5, C2×D42D5, C22×C5⋊D4, C2×Dic5⋊D4

Smallest permutation representation of 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 78)(12 79)(13 80)(14 71)(15 72)(16 73)(17 74)(18 75)(19 76)(20 77)(21 94)(22 95)(23 96)(24 97)(25 98)(26 99)(27 100)(28 91)(29 92)(30 93)(31 128)(32 129)(33 130)(34 121)(35 122)(36 123)(37 124)(38 125)(39 126)(40 127)(41 114)(42 115)(43 116)(44 117)(45 118)(46 119)(47 120)(48 111)(49 112)(50 113)(51 148)(52 149)(53 150)(54 141)(55 142)(56 143)(57 144)(58 145)(59 146)(60 147)(61 134)(62 135)(63 136)(64 137)(65 138)(66 139)(67 140)(68 131)(69 132)(70 133)(81 154)(82 155)(83 156)(84 157)(85 158)(86 159)(87 160)(88 151)(89 152)(90 153)
(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)(11 137 16 132)(12 136 17 131)(13 135 18 140)(14 134 19 139)(15 133 20 138)(21 36 26 31)(22 35 27 40)(23 34 28 39)(24 33 29 38)(25 32 30 37)(51 86 56 81)(52 85 57 90)(53 84 58 89)(54 83 59 88)(55 82 60 87)(61 76 66 71)(62 75 67 80)(63 74 68 79)(64 73 69 78)(65 72 70 77)(91 126 96 121)(92 125 97 130)(93 124 98 129)(94 123 99 128)(95 122 100 127)(101 116 106 111)(102 115 107 120)(103 114 108 119)(104 113 109 118)(105 112 110 117)(141 156 146 151)(142 155 147 160)(143 154 148 159)(144 153 149 158)(145 152 150 157)
(1 87 27 80)(2 88 28 71)(3 89 29 72)(4 90 30 73)(5 81 21 74)(6 82 22 75)(7 83 23 76)(8 84 24 77)(9 85 25 78)(10 86 26 79)(11 105 158 98)(12 106 159 99)(13 107 160 100)(14 108 151 91)(15 109 152 92)(16 110 153 93)(17 101 154 94)(18 102 155 95)(19 103 156 96)(20 104 157 97)(31 68 48 51)(32 69 49 52)(33 70 50 53)(34 61 41 54)(35 62 42 55)(36 63 43 56)(37 64 44 57)(38 65 45 58)(39 66 46 59)(40 67 47 60)(111 148 128 131)(112 149 129 132)(113 150 130 133)(114 141 121 134)(115 142 122 135)(116 143 123 136)(117 144 124 137)(118 145 125 138)(119 146 126 139)(120 147 127 140)
(1 60)(2 51)(3 52)(4 53)(5 54)(6 55)(7 56)(8 57)(9 58)(10 59)(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)(11,78)(12,79)(13,80)(14,71)(15,72)(16,73)(17,74)(18,75)(19,76)(20,77)(21,94)(22,95)(23,96)(24,97)(25,98)(26,99)(27,100)(28,91)(29,92)(30,93)(31,128)(32,129)(33,130)(34,121)(35,122)(36,123)(37,124)(38,125)(39,126)(40,127)(41,114)(42,115)(43,116)(44,117)(45,118)(46,119)(47,120)(48,111)(49,112)(50,113)(51,148)(52,149)(53,150)(54,141)(55,142)(56,143)(57,144)(58,145)(59,146)(60,147)(61,134)(62,135)(63,136)(64,137)(65,138)(66,139)(67,140)(68,131)(69,132)(70,133)(81,154)(82,155)(83,156)(84,157)(85,158)(86,159)(87,160)(88,151)(89,152)(90,153), (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)(11,137,16,132)(12,136,17,131)(13,135,18,140)(14,134,19,139)(15,133,20,138)(21,36,26,31)(22,35,27,40)(23,34,28,39)(24,33,29,38)(25,32,30,37)(51,86,56,81)(52,85,57,90)(53,84,58,89)(54,83,59,88)(55,82,60,87)(61,76,66,71)(62,75,67,80)(63,74,68,79)(64,73,69,78)(65,72,70,77)(91,126,96,121)(92,125,97,130)(93,124,98,129)(94,123,99,128)(95,122,100,127)(101,116,106,111)(102,115,107,120)(103,114,108,119)(104,113,109,118)(105,112,110,117)(141,156,146,151)(142,155,147,160)(143,154,148,159)(144,153,149,158)(145,152,150,157), (1,87,27,80)(2,88,28,71)(3,89,29,72)(4,90,30,73)(5,81,21,74)(6,82,22,75)(7,83,23,76)(8,84,24,77)(9,85,25,78)(10,86,26,79)(11,105,158,98)(12,106,159,99)(13,107,160,100)(14,108,151,91)(15,109,152,92)(16,110,153,93)(17,101,154,94)(18,102,155,95)(19,103,156,96)(20,104,157,97)(31,68,48,51)(32,69,49,52)(33,70,50,53)(34,61,41,54)(35,62,42,55)(36,63,43,56)(37,64,44,57)(38,65,45,58)(39,66,46,59)(40,67,47,60)(111,148,128,131)(112,149,129,132)(113,150,130,133)(114,141,121,134)(115,142,122,135)(116,143,123,136)(117,144,124,137)(118,145,125,138)(119,146,126,139)(120,147,127,140), (1,60)(2,51)(3,52)(4,53)(5,54)(6,55)(7,56)(8,57)(9,58)(10,59)(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)(11,78)(12,79)(13,80)(14,71)(15,72)(16,73)(17,74)(18,75)(19,76)(20,77)(21,94)(22,95)(23,96)(24,97)(25,98)(26,99)(27,100)(28,91)(29,92)(30,93)(31,128)(32,129)(33,130)(34,121)(35,122)(36,123)(37,124)(38,125)(39,126)(40,127)(41,114)(42,115)(43,116)(44,117)(45,118)(46,119)(47,120)(48,111)(49,112)(50,113)(51,148)(52,149)(53,150)(54,141)(55,142)(56,143)(57,144)(58,145)(59,146)(60,147)(61,134)(62,135)(63,136)(64,137)(65,138)(66,139)(67,140)(68,131)(69,132)(70,133)(81,154)(82,155)(83,156)(84,157)(85,158)(86,159)(87,160)(88,151)(89,152)(90,153), (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)(11,137,16,132)(12,136,17,131)(13,135,18,140)(14,134,19,139)(15,133,20,138)(21,36,26,31)(22,35,27,40)(23,34,28,39)(24,33,29,38)(25,32,30,37)(51,86,56,81)(52,85,57,90)(53,84,58,89)(54,83,59,88)(55,82,60,87)(61,76,66,71)(62,75,67,80)(63,74,68,79)(64,73,69,78)(65,72,70,77)(91,126,96,121)(92,125,97,130)(93,124,98,129)(94,123,99,128)(95,122,100,127)(101,116,106,111)(102,115,107,120)(103,114,108,119)(104,113,109,118)(105,112,110,117)(141,156,146,151)(142,155,147,160)(143,154,148,159)(144,153,149,158)(145,152,150,157), (1,87,27,80)(2,88,28,71)(3,89,29,72)(4,90,30,73)(5,81,21,74)(6,82,22,75)(7,83,23,76)(8,84,24,77)(9,85,25,78)(10,86,26,79)(11,105,158,98)(12,106,159,99)(13,107,160,100)(14,108,151,91)(15,109,152,92)(16,110,153,93)(17,101,154,94)(18,102,155,95)(19,103,156,96)(20,104,157,97)(31,68,48,51)(32,69,49,52)(33,70,50,53)(34,61,41,54)(35,62,42,55)(36,63,43,56)(37,64,44,57)(38,65,45,58)(39,66,46,59)(40,67,47,60)(111,148,128,131)(112,149,129,132)(113,150,130,133)(114,141,121,134)(115,142,122,135)(116,143,123,136)(117,144,124,137)(118,145,125,138)(119,146,126,139)(120,147,127,140), (1,60)(2,51)(3,52)(4,53)(5,54)(6,55)(7,56)(8,57)(9,58)(10,59)(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),(11,78),(12,79),(13,80),(14,71),(15,72),(16,73),(17,74),(18,75),(19,76),(20,77),(21,94),(22,95),(23,96),(24,97),(25,98),(26,99),(27,100),(28,91),(29,92),(30,93),(31,128),(32,129),(33,130),(34,121),(35,122),(36,123),(37,124),(38,125),(39,126),(40,127),(41,114),(42,115),(43,116),(44,117),(45,118),(46,119),(47,120),(48,111),(49,112),(50,113),(51,148),(52,149),(53,150),(54,141),(55,142),(56,143),(57,144),(58,145),(59,146),(60,147),(61,134),(62,135),(63,136),(64,137),(65,138),(66,139),(67,140),(68,131),(69,132),(70,133),(81,154),(82,155),(83,156),(84,157),(85,158),(86,159),(87,160),(88,151),(89,152),(90,153)], [(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),(11,137,16,132),(12,136,17,131),(13,135,18,140),(14,134,19,139),(15,133,20,138),(21,36,26,31),(22,35,27,40),(23,34,28,39),(24,33,29,38),(25,32,30,37),(51,86,56,81),(52,85,57,90),(53,84,58,89),(54,83,59,88),(55,82,60,87),(61,76,66,71),(62,75,67,80),(63,74,68,79),(64,73,69,78),(65,72,70,77),(91,126,96,121),(92,125,97,130),(93,124,98,129),(94,123,99,128),(95,122,100,127),(101,116,106,111),(102,115,107,120),(103,114,108,119),(104,113,109,118),(105,112,110,117),(141,156,146,151),(142,155,147,160),(143,154,148,159),(144,153,149,158),(145,152,150,157)], [(1,87,27,80),(2,88,28,71),(3,89,29,72),(4,90,30,73),(5,81,21,74),(6,82,22,75),(7,83,23,76),(8,84,24,77),(9,85,25,78),(10,86,26,79),(11,105,158,98),(12,106,159,99),(13,107,160,100),(14,108,151,91),(15,109,152,92),(16,110,153,93),(17,101,154,94),(18,102,155,95),(19,103,156,96),(20,104,157,97),(31,68,48,51),(32,69,49,52),(33,70,50,53),(34,61,41,54),(35,62,42,55),(36,63,43,56),(37,64,44,57),(38,65,45,58),(39,66,46,59),(40,67,47,60),(111,148,128,131),(112,149,129,132),(113,150,130,133),(114,141,121,134),(115,142,122,135),(116,143,123,136),(117,144,124,137),(118,145,125,138),(119,146,126,139),(120,147,127,140)], [(1,60),(2,51),(3,52),(4,53),(5,54),(6,55),(7,56),(8,57),(9,58),(10,59),(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···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×D5D42D5
kernelC2×Dic5⋊D4C2×C10.D4C2×D10⋊C4Dic5⋊D4C2×C23.D5C23×Dic5C22×C5⋊D4D4×C2×C10C2×Dic5C22×C10C22×D4C2×C10C22×C4C2×D4C24C23C22C22
# reps1118112144242841644

Matrix representation of C2×Dic5⋊D4 in 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] >;

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

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