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## G = C2×Dic5⋊4D4order 320 = 26·5

### Direct product of C2 and Dic5⋊4D4

Series: Derived Chief Lower central Upper central

 Derived series C1 — C10 — C2×Dic5⋊4D4
 Chief series C1 — C5 — C10 — C2×C10 — C22×D5 — C23×D5 — C22×C5⋊D4 — C2×Dic5⋊4D4
 Lower central C5 — C10 — C2×Dic5⋊4D4
 Upper central C1 — C23 — C2×C22⋊C4

Generators and relations for C2×Dic54D4
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 [×3], C2 [×4], C2 [×8], C4 [×14], C22, C22 [×10], C22 [×28], C5, C2×C4 [×4], C2×C4 [×36], D4 [×16], C23, C23 [×6], C23 [×14], D5 [×4], C10 [×3], C10 [×4], C10 [×4], C42 [×4], C22⋊C4 [×4], C22⋊C4 [×4], C4⋊C4 [×4], C22×C4 [×2], C22×C4 [×19], C2×D4 [×12], C24, C24, Dic5 [×8], Dic5 [×2], C20 [×4], D10 [×4], D10 [×12], C2×C10, C2×C10 [×10], C2×C10 [×12], C2×C42, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C4×D4 [×8], C23×C4 [×2], C22×D4, C4×D5 [×8], C2×Dic5 [×14], C2×Dic5 [×10], C5⋊D4 [×16], C2×C20 [×4], C2×C20 [×4], C22×D5 [×6], C22×D5 [×4], C22×C10, C22×C10 [×6], C22×C10 [×4], C2×C4×D4, C4×Dic5 [×4], C10.D4 [×4], D10⋊C4 [×4], C5×C22⋊C4 [×4], C2×C4×D5 [×4], C2×C4×D5 [×4], C22×Dic5 [×3], C22×Dic5 [×4], C22×Dic5 [×4], C2×C5⋊D4 [×12], C22×C20 [×2], C23×D5, C23×C10, Dic54D4 [×8], C2×C4×Dic5, C2×C10.D4, C2×D10⋊C4, C10×C22⋊C4, D5×C22×C4, C23×Dic5, C22×C5⋊D4, C2×Dic54D4
Quotients: C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], D4 [×4], C23 [×15], D5, C22×C4 [×14], C2×D4 [×6], C4○D4 [×2], C24, D10 [×7], C4×D4 [×4], C23×C4, C22×D4, C2×C4○D4, C4×D5 [×4], C22×D5 [×7], C2×C4×D4, C2×C4×D5 [×6], D4×D5 [×2], D42D5 [×2], C23×D5, Dic54D4 [×4], D5×C22×C4, C2×D4×D5, C2×D42D5, C2×Dic54D4

Smallest permutation representation of C2×Dic54D4
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 42 6 47)(2 41 7 46)(3 50 8 45)(4 49 9 44)(5 48 10 43)(11 132 16 137)(12 131 17 136)(13 140 18 135)(14 139 19 134)(15 138 20 133)(21 31 26 36)(22 40 27 35)(23 39 28 34)(24 38 29 33)(25 37 30 32)(51 81 56 86)(52 90 57 85)(53 89 58 84)(54 88 59 83)(55 87 60 82)(61 71 66 76)(62 80 67 75)(63 79 68 74)(64 78 69 73)(65 77 70 72)(91 121 96 126)(92 130 97 125)(93 129 98 124)(94 128 99 123)(95 127 100 122)(101 111 106 116)(102 120 107 115)(103 119 108 114)(104 118 109 113)(105 117 110 112)(141 151 146 156)(142 160 147 155)(143 159 148 154)(144 158 149 153)(145 157 150 152)
(1 140 27 147)(2 139 28 146)(3 138 29 145)(4 137 30 144)(5 136 21 143)(6 135 22 142)(7 134 23 141)(8 133 24 150)(9 132 25 149)(10 131 26 148)(11 32 158 49)(12 31 159 48)(13 40 160 47)(14 39 151 46)(15 38 152 45)(16 37 153 44)(17 36 154 43)(18 35 155 42)(19 34 156 41)(20 33 157 50)(51 106 68 99)(52 105 69 98)(53 104 70 97)(54 103 61 96)(55 102 62 95)(56 101 63 94)(57 110 64 93)(58 109 65 92)(59 108 66 91)(60 107 67 100)(71 126 88 119)(72 125 89 118)(73 124 90 117)(74 123 81 116)(75 122 82 115)(76 121 83 114)(77 130 84 113)(78 129 85 112)(79 128 86 111)(80 127 87 120)
(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), (1,42,6,47)(2,41,7,46)(3,50,8,45)(4,49,9,44)(5,48,10,43)(11,132,16,137)(12,131,17,136)(13,140,18,135)(14,139,19,134)(15,138,20,133)(21,31,26,36)(22,40,27,35)(23,39,28,34)(24,38,29,33)(25,37,30,32)(51,81,56,86)(52,90,57,85)(53,89,58,84)(54,88,59,83)(55,87,60,82)(61,71,66,76)(62,80,67,75)(63,79,68,74)(64,78,69,73)(65,77,70,72)(91,121,96,126)(92,130,97,125)(93,129,98,124)(94,128,99,123)(95,127,100,122)(101,111,106,116)(102,120,107,115)(103,119,108,114)(104,118,109,113)(105,117,110,112)(141,151,146,156)(142,160,147,155)(143,159,148,154)(144,158,149,153)(145,157,150,152), (1,140,27,147)(2,139,28,146)(3,138,29,145)(4,137,30,144)(5,136,21,143)(6,135,22,142)(7,134,23,141)(8,133,24,150)(9,132,25,149)(10,131,26,148)(11,32,158,49)(12,31,159,48)(13,40,160,47)(14,39,151,46)(15,38,152,45)(16,37,153,44)(17,36,154,43)(18,35,155,42)(19,34,156,41)(20,33,157,50)(51,106,68,99)(52,105,69,98)(53,104,70,97)(54,103,61,96)(55,102,62,95)(56,101,63,94)(57,110,64,93)(58,109,65,92)(59,108,66,91)(60,107,67,100)(71,126,88,119)(72,125,89,118)(73,124,90,117)(74,123,81,116)(75,122,82,115)(76,121,83,114)(77,130,84,113)(78,129,85,112)(79,128,86,111)(80,127,87,120), (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), (1,42,6,47)(2,41,7,46)(3,50,8,45)(4,49,9,44)(5,48,10,43)(11,132,16,137)(12,131,17,136)(13,140,18,135)(14,139,19,134)(15,138,20,133)(21,31,26,36)(22,40,27,35)(23,39,28,34)(24,38,29,33)(25,37,30,32)(51,81,56,86)(52,90,57,85)(53,89,58,84)(54,88,59,83)(55,87,60,82)(61,71,66,76)(62,80,67,75)(63,79,68,74)(64,78,69,73)(65,77,70,72)(91,121,96,126)(92,130,97,125)(93,129,98,124)(94,128,99,123)(95,127,100,122)(101,111,106,116)(102,120,107,115)(103,119,108,114)(104,118,109,113)(105,117,110,112)(141,151,146,156)(142,160,147,155)(143,159,148,154)(144,158,149,153)(145,157,150,152), (1,140,27,147)(2,139,28,146)(3,138,29,145)(4,137,30,144)(5,136,21,143)(6,135,22,142)(7,134,23,141)(8,133,24,150)(9,132,25,149)(10,131,26,148)(11,32,158,49)(12,31,159,48)(13,40,160,47)(14,39,151,46)(15,38,152,45)(16,37,153,44)(17,36,154,43)(18,35,155,42)(19,34,156,41)(20,33,157,50)(51,106,68,99)(52,105,69,98)(53,104,70,97)(54,103,61,96)(55,102,62,95)(56,101,63,94)(57,110,64,93)(58,109,65,92)(59,108,66,91)(60,107,67,100)(71,126,88,119)(72,125,89,118)(73,124,90,117)(74,123,81,116)(75,122,82,115)(76,121,83,114)(77,130,84,113)(78,129,85,112)(79,128,86,111)(80,127,87,120), (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)], [(1,42,6,47),(2,41,7,46),(3,50,8,45),(4,49,9,44),(5,48,10,43),(11,132,16,137),(12,131,17,136),(13,140,18,135),(14,139,19,134),(15,138,20,133),(21,31,26,36),(22,40,27,35),(23,39,28,34),(24,38,29,33),(25,37,30,32),(51,81,56,86),(52,90,57,85),(53,89,58,84),(54,88,59,83),(55,87,60,82),(61,71,66,76),(62,80,67,75),(63,79,68,74),(64,78,69,73),(65,77,70,72),(91,121,96,126),(92,130,97,125),(93,129,98,124),(94,128,99,123),(95,127,100,122),(101,111,106,116),(102,120,107,115),(103,119,108,114),(104,118,109,113),(105,117,110,112),(141,151,146,156),(142,160,147,155),(143,159,148,154),(144,158,149,153),(145,157,150,152)], [(1,140,27,147),(2,139,28,146),(3,138,29,145),(4,137,30,144),(5,136,21,143),(6,135,22,142),(7,134,23,141),(8,133,24,150),(9,132,25,149),(10,131,26,148),(11,32,158,49),(12,31,159,48),(13,40,160,47),(14,39,151,46),(15,38,152,45),(16,37,153,44),(17,36,154,43),(18,35,155,42),(19,34,156,41),(20,33,157,50),(51,106,68,99),(52,105,69,98),(53,104,70,97),(54,103,61,96),(55,102,62,95),(56,101,63,94),(57,110,64,93),(58,109,65,92),(59,108,66,91),(60,107,67,100),(71,126,88,119),(72,125,89,118),(73,124,90,117),(74,123,81,116),(75,122,82,115),(76,121,83,114),(77,130,84,113),(78,129,85,112),(79,128,86,111),(80,127,87,120)], [(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)])

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×Dic54D4 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×Dic54D4 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

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