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G = C2×C4⋊C47D5order 320 = 26·5

Direct product of C2 and C4⋊C47D5

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C2×C4⋊C47D5, C4⋊C451D10, C10.33(C23×C4), (C2×C10).46C24, C4⋊Dic570C22, C104(C42⋊C2), (C2×C20).578C23, C20.147(C22×C4), (C4×Dic5)⋊75C22, D10.40(C22×C4), (C22×C4).359D10, C22.22(C23×D5), Dic5.53(C22×C4), C23.325(C22×D5), C22.73(D42D5), (C22×C10).395C23, (C22×C20).358C22, C22.33(Q82D5), (C2×Dic5).195C23, (C22×D5).163C23, (C23×D5).109C22, D10⋊C4.115C22, (C22×Dic5).233C22, (C2×C4×D5)⋊9C4, (C10×C4⋊C4)⋊8C2, C4.91(C2×C4×D5), (C2×C4⋊C4)⋊25D5, (C4×D5)⋊16(C2×C4), C54(C2×C42⋊C2), (C2×C4×Dic5)⋊32C2, (D5×C22×C4).4C2, (C5×C4⋊C4)⋊43C22, C2.14(D5×C22×C4), C22.72(C2×C4×D5), (C2×C4⋊Dic5)⋊38C2, C10.71(C2×C4○D4), C2.4(C2×D42D5), (C2×C4).161(C4×D5), C2.1(C2×Q82D5), (C2×C20).301(C2×C4), (C2×C4×D5).313C22, (C2×C4).265(C22×D5), (C2×D10⋊C4).25C2, (C2×C10).171(C4○D4), (C2×C10).252(C22×C4), (C2×Dic5).207(C2×C4), (C22×D5).109(C2×C4), SmallGroup(320,1174)

Series: Derived Chief Lower central Upper central

C1C10 — C2×C4⋊C47D5
C1C5C10C2×C10C22×D5C23×D5D5×C22×C4 — C2×C4⋊C47D5
C5C10 — C2×C4⋊C47D5
C1C23C2×C4⋊C4

Generators and relations for C2×C4⋊C47D5
 G = < a,b,c,d,e | a2=b4=c4=d5=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, cd=dc, ece=b2c, ede=d-1 >

Subgroups: 990 in 330 conjugacy classes, 167 normal (21 characteristic)
C1, C2 [×3], C2 [×4], C2 [×4], C4 [×4], C4 [×12], C22, C22 [×6], C22 [×16], C5, C2×C4 [×10], C2×C4 [×34], C23, C23 [×10], D5 [×4], C10 [×3], C10 [×4], C42 [×8], C22⋊C4 [×8], C4⋊C4 [×4], C4⋊C4 [×4], C22×C4, C22×C4 [×2], C22×C4 [×15], C24, Dic5 [×4], Dic5 [×4], C20 [×4], C20 [×4], D10 [×4], D10 [×12], C2×C10, C2×C10 [×6], C2×C42 [×2], C2×C22⋊C4 [×2], C2×C4⋊C4, C2×C4⋊C4, C42⋊C2 [×8], C23×C4, C4×D5 [×16], C2×Dic5 [×10], C2×Dic5 [×4], C2×C20 [×10], C2×C20 [×4], C22×D5 [×6], C22×D5 [×4], C22×C10, C2×C42⋊C2, C4×Dic5 [×8], C4⋊Dic5 [×4], D10⋊C4 [×8], C5×C4⋊C4 [×4], C2×C4×D5 [×12], C22×Dic5, C22×Dic5 [×2], C22×C20, C22×C20 [×2], C23×D5, C4⋊C47D5 [×8], C2×C4×Dic5 [×2], C2×C4⋊Dic5, C2×D10⋊C4 [×2], C10×C4⋊C4, D5×C22×C4, C2×C4⋊C47D5
Quotients: C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], C23 [×15], D5, C22×C4 [×14], C4○D4 [×4], C24, D10 [×7], C42⋊C2 [×4], C23×C4, C2×C4○D4 [×2], C4×D5 [×4], C22×D5 [×7], C2×C42⋊C2, C2×C4×D5 [×6], D42D5 [×2], Q82D5 [×2], C23×D5, C4⋊C47D5 [×4], D5×C22×C4, C2×D42D5, C2×Q82D5, C2×C4⋊C47D5

Smallest permutation representation of C2×C4⋊C47D5
On 160 points
Generators in S160
(1 96)(2 97)(3 98)(4 99)(5 100)(6 91)(7 92)(8 93)(9 94)(10 95)(11 86)(12 87)(13 88)(14 89)(15 90)(16 81)(17 82)(18 83)(19 84)(20 85)(21 116)(22 117)(23 118)(24 119)(25 120)(26 111)(27 112)(28 113)(29 114)(30 115)(31 106)(32 107)(33 108)(34 109)(35 110)(36 101)(37 102)(38 103)(39 104)(40 105)(41 136)(42 137)(43 138)(44 139)(45 140)(46 131)(47 132)(48 133)(49 134)(50 135)(51 126)(52 127)(53 128)(54 129)(55 130)(56 121)(57 122)(58 123)(59 124)(60 125)(61 156)(62 157)(63 158)(64 159)(65 160)(66 151)(67 152)(68 153)(69 154)(70 155)(71 146)(72 147)(73 148)(74 149)(75 150)(76 141)(77 142)(78 143)(79 144)(80 145)
(1 131 6 136)(2 132 7 137)(3 133 8 138)(4 134 9 139)(5 135 10 140)(11 121 16 126)(12 122 17 127)(13 123 18 128)(14 124 19 129)(15 125 20 130)(21 151 26 156)(22 152 27 157)(23 153 28 158)(24 154 29 159)(25 155 30 160)(31 141 36 146)(32 142 37 147)(33 143 38 148)(34 144 39 149)(35 145 40 150)(41 96 46 91)(42 97 47 92)(43 98 48 93)(44 99 49 94)(45 100 50 95)(51 86 56 81)(52 87 57 82)(53 88 58 83)(54 89 59 84)(55 90 60 85)(61 116 66 111)(62 117 67 112)(63 118 68 113)(64 119 69 114)(65 120 70 115)(71 106 76 101)(72 107 77 102)(73 108 78 103)(74 109 79 104)(75 110 80 105)
(1 71 11 61)(2 72 12 62)(3 73 13 63)(4 74 14 64)(5 75 15 65)(6 76 16 66)(7 77 17 67)(8 78 18 68)(9 79 19 69)(10 80 20 70)(21 41 31 51)(22 42 32 52)(23 43 33 53)(24 44 34 54)(25 45 35 55)(26 46 36 56)(27 47 37 57)(28 48 38 58)(29 49 39 59)(30 50 40 60)(81 151 91 141)(82 152 92 142)(83 153 93 143)(84 154 94 144)(85 155 95 145)(86 156 96 146)(87 157 97 147)(88 158 98 148)(89 159 99 149)(90 160 100 150)(101 121 111 131)(102 122 112 132)(103 123 113 133)(104 124 114 134)(105 125 115 135)(106 126 116 136)(107 127 117 137)(108 128 118 138)(109 129 119 139)(110 130 120 140)
(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 95)(2 94)(3 93)(4 92)(5 91)(6 100)(7 99)(8 98)(9 97)(10 96)(11 85)(12 84)(13 83)(14 82)(15 81)(16 90)(17 89)(18 88)(19 87)(20 86)(21 120)(22 119)(23 118)(24 117)(25 116)(26 115)(27 114)(28 113)(29 112)(30 111)(31 110)(32 109)(33 108)(34 107)(35 106)(36 105)(37 104)(38 103)(39 102)(40 101)(41 135)(42 134)(43 133)(44 132)(45 131)(46 140)(47 139)(48 138)(49 137)(50 136)(51 125)(52 124)(53 123)(54 122)(55 121)(56 130)(57 129)(58 128)(59 127)(60 126)(61 160)(62 159)(63 158)(64 157)(65 156)(66 155)(67 154)(68 153)(69 152)(70 151)(71 150)(72 149)(73 148)(74 147)(75 146)(76 145)(77 144)(78 143)(79 142)(80 141)

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

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

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

80 conjugacy classes

class 1 2A···2G2H2I2J2K4A···4L4M···4T4U···4AB5A5B10A···10N20A···20X
order12···222224···44···44···45510···1020···20
size11···1101010102···25···510···10222···24···4

80 irreducible representations

dim111111112222244
type++++++++++-+
imageC1C2C2C2C2C2C2C4D5C4○D4D10D10C4×D5D42D5Q82D5
kernelC2×C4⋊C47D5C4⋊C47D5C2×C4×Dic5C2×C4⋊Dic5C2×D10⋊C4C10×C4⋊C4D5×C22×C4C2×C4×D5C2×C4⋊C4C2×C10C4⋊C4C22×C4C2×C4C22C22
# reps18212111628861644

Matrix representation of C2×C4⋊C47D5 in GL6(𝔽41)

100000
010000
0040000
0004000
000010
000001
,
100000
010000
001000
000100
000090
00002332
,
3200000
0320000
0032000
0003200
000011
0000040
,
3550000
1400000
0064000
001000
000010
000001
,
0350000
3400000
0035100
006600
0000400
000021

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],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,9,23,0,0,0,0,0,32],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,32,0,0,0,0,0,0,32,0,0,0,0,0,0,1,0,0,0,0,0,1,40],[35,1,0,0,0,0,5,40,0,0,0,0,0,0,6,1,0,0,0,0,40,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,34,0,0,0,0,35,0,0,0,0,0,0,0,35,6,0,0,0,0,1,6,0,0,0,0,0,0,40,2,0,0,0,0,0,1] >;

C2×C4⋊C47D5 in GAP, Magma, Sage, TeX

C_2\times C_4\rtimes C_4\rtimes_7D_5
% in TeX

G:=Group("C2xC4:C4:7D5");
// GroupNames label

G:=SmallGroup(320,1174);
// by ID

G=gap.SmallGroup(320,1174);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,184,1123,297,80,12550]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^4=c^4=d^5=e^2=1,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,c*d=d*c,e*c*e=b^2*c,e*d*e=d^-1>;
// generators/relations

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