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## G = C2×Q16⋊D5order 320 = 26·5

### Direct product of C2 and Q16⋊D5

Series: Derived Chief Lower central Upper central

 Derived series C1 — C20 — C2×Q16⋊D5
 Chief series C1 — C5 — C10 — C20 — C4×D5 — C2×C4×D5 — C2×Q8×D5 — C2×Q16⋊D5
 Lower central C5 — C10 — C20 — C2×Q16⋊D5
 Upper central C1 — C22 — C2×C4 — C2×Q16

Generators and relations for C2×Q16⋊D5
G = < a,b,c,d,e | a2=b8=d5=e2=1, c2=b4, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, ebe=b5, cd=dc, ece=b4c, ede=d-1 >

Subgroups: 958 in 258 conjugacy classes, 103 normal (33 characteristic)
C1, C2, C2 [×2], C2 [×4], C4 [×2], C4 [×8], C22, C22 [×8], C5, C8 [×2], C8 [×2], C2×C4, C2×C4 [×16], D4 [×7], Q8 [×4], Q8 [×9], C23 [×2], D5 [×4], C10, C10 [×2], C2×C8, C2×C8, M4(2) [×4], SD16 [×8], Q16 [×4], Q16 [×4], C22×C4 [×3], C2×D4 [×2], C2×Q8 [×2], C2×Q8 [×8], C4○D4 [×6], Dic5 [×2], Dic5 [×2], C20 [×2], C20 [×4], D10 [×2], D10 [×6], C2×C10, C2×M4(2), C2×SD16 [×2], C2×Q16, C2×Q16, C8.C22 [×8], C22×Q8, C2×C4○D4, C52C8 [×2], C40 [×2], Dic10 [×2], Dic10 [×5], C4×D5 [×4], C4×D5 [×8], D20 [×2], D20 [×5], C2×Dic5, C2×Dic5, C2×C20, C2×C20 [×2], C5×Q8 [×4], C5×Q8 [×2], C22×D5, C22×D5, C2×C8.C22, C8⋊D5 [×4], C40⋊C2 [×4], C2×C52C8, Q8⋊D5 [×4], C5⋊Q16 [×4], C2×C40, C5×Q16 [×4], C2×Dic10, C2×Dic10, C2×C4×D5, C2×C4×D5 [×2], C2×D20, C2×D20, Q8×D5 [×4], Q8×D5 [×2], Q82D5 [×4], Q82D5 [×2], Q8×C10 [×2], C2×C8⋊D5, C2×C40⋊C2, Q16⋊D5 [×8], C2×Q8⋊D5, C2×C5⋊Q16, C10×Q16, C2×Q8×D5, C2×Q82D5, C2×Q16⋊D5
Quotients: C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D5, C2×D4 [×6], C24, D10 [×7], C8.C22 [×2], C22×D4, C22×D5 [×7], C2×C8.C22, D4×D5 [×2], C23×D5, Q16⋊D5 [×2], C2×D4×D5, C2×Q16⋊D5

Smallest permutation representation of C2×Q16⋊D5
On 160 points
Generators in S160
(1 98)(2 99)(3 100)(4 101)(5 102)(6 103)(7 104)(8 97)(9 107)(10 108)(11 109)(12 110)(13 111)(14 112)(15 105)(16 106)(17 157)(18 158)(19 159)(20 160)(21 153)(22 154)(23 155)(24 156)(25 149)(26 150)(27 151)(28 152)(29 145)(30 146)(31 147)(32 148)(33 138)(34 139)(35 140)(36 141)(37 142)(38 143)(39 144)(40 137)(41 85)(42 86)(43 87)(44 88)(45 81)(46 82)(47 83)(48 84)(49 91)(50 92)(51 93)(52 94)(53 95)(54 96)(55 89)(56 90)(57 132)(58 133)(59 134)(60 135)(61 136)(62 129)(63 130)(64 131)(65 128)(66 121)(67 122)(68 123)(69 124)(70 125)(71 126)(72 127)(73 113)(74 114)(75 115)(76 116)(77 117)(78 118)(79 119)(80 120)
(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 77 5 73)(2 76 6 80)(3 75 7 79)(4 74 8 78)(9 28 13 32)(10 27 14 31)(11 26 15 30)(12 25 16 29)(17 140 21 144)(18 139 22 143)(19 138 23 142)(20 137 24 141)(33 155 37 159)(34 154 38 158)(35 153 39 157)(36 160 40 156)(41 65 45 69)(42 72 46 68)(43 71 47 67)(44 70 48 66)(49 59 53 63)(50 58 54 62)(51 57 55 61)(52 64 56 60)(81 124 85 128)(82 123 86 127)(83 122 87 126)(84 121 88 125)(89 136 93 132)(90 135 94 131)(91 134 95 130)(92 133 96 129)(97 118 101 114)(98 117 102 113)(99 116 103 120)(100 115 104 119)(105 146 109 150)(106 145 110 149)(107 152 111 148)(108 151 112 147)
(1 107 33 128 133)(2 108 34 121 134)(3 109 35 122 135)(4 110 36 123 136)(5 111 37 124 129)(6 112 38 125 130)(7 105 39 126 131)(8 106 40 127 132)(9 138 65 58 98)(10 139 66 59 99)(11 140 67 60 100)(12 141 68 61 101)(13 142 69 62 102)(14 143 70 63 103)(15 144 71 64 104)(16 137 72 57 97)(17 47 56 119 30)(18 48 49 120 31)(19 41 50 113 32)(20 42 51 114 25)(21 43 52 115 26)(22 44 53 116 27)(23 45 54 117 28)(24 46 55 118 29)(73 148 159 85 92)(74 149 160 86 93)(75 150 153 87 94)(76 151 154 88 95)(77 152 155 81 96)(78 145 156 82 89)(79 146 157 83 90)(80 147 158 84 91)
(1 92)(2 89)(3 94)(4 91)(5 96)(6 93)(7 90)(8 95)(9 41)(10 46)(11 43)(12 48)(13 45)(14 42)(15 47)(16 44)(17 144)(18 141)(19 138)(20 143)(21 140)(22 137)(23 142)(24 139)(25 70)(26 67)(27 72)(28 69)(29 66)(30 71)(31 68)(32 65)(33 159)(34 156)(35 153)(36 158)(37 155)(38 160)(39 157)(40 154)(49 101)(50 98)(51 103)(52 100)(53 97)(54 102)(55 99)(56 104)(57 116)(58 113)(59 118)(60 115)(61 120)(62 117)(63 114)(64 119)(73 133)(74 130)(75 135)(76 132)(77 129)(78 134)(79 131)(80 136)(81 111)(82 108)(83 105)(84 110)(85 107)(86 112)(87 109)(88 106)(121 145)(122 150)(123 147)(124 152)(125 149)(126 146)(127 151)(128 148)

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

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

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

50 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 20A 20B 20C 20D 20E ··· 20L 40A ··· 40H 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 20 20 20 20 20 ··· 20 40 ··· 40 size 1 1 1 1 10 10 20 20 2 2 4 4 4 4 10 10 20 20 2 2 4 4 20 20 2 ··· 2 4 4 4 4 8 ··· 8 4 ··· 4

50 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 4 4 4 4 type + + + + + + + + + + + + + + + + - + + image C1 C2 C2 C2 C2 C2 C2 C2 C2 D4 D4 D4 D5 D10 D10 D10 C8.C22 D4×D5 D4×D5 Q16⋊D5 kernel C2×Q16⋊D5 C2×C8⋊D5 C2×C40⋊C2 Q16⋊D5 C2×Q8⋊D5 C2×C5⋊Q16 C10×Q16 C2×Q8×D5 C2×Q8⋊2D5 C4×D5 C2×Dic5 C22×D5 C2×Q16 C2×C8 Q16 C2×Q8 C10 C4 C22 C2 # reps 1 1 1 8 1 1 1 1 1 2 1 1 2 2 8 4 2 2 2 8

Matrix representation of C2×Q16⋊D5 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
,
 40 0 0 0 0 0 0 40 0 0 0 0 0 0 39 17 2 24 0 0 24 2 17 39 0 0 40 29 0 0 0 0 12 1 0 0
,
 40 0 0 0 0 0 0 40 0 0 0 0 0 0 6 40 22 0 0 0 1 13 0 22 0 0 17 40 35 1 0 0 1 24 40 28
,
 40 40 0 0 0 0 36 35 0 0 0 0 0 0 34 40 0 0 0 0 1 0 0 0 0 0 0 0 34 40 0 0 0 0 1 0
,
 0 7 0 0 0 0 6 0 0 0 0 0 0 0 39 35 10 19 0 0 8 2 31 31 0 0 36 11 8 13 0 0 5 5 39 33

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],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,39,24,40,12,0,0,17,2,29,1,0,0,2,17,0,0,0,0,24,39,0,0],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,6,1,17,1,0,0,40,13,40,24,0,0,22,0,35,40,0,0,0,22,1,28],[40,36,0,0,0,0,40,35,0,0,0,0,0,0,34,1,0,0,0,0,40,0,0,0,0,0,0,0,34,1,0,0,0,0,40,0],[0,6,0,0,0,0,7,0,0,0,0,0,0,0,39,8,36,5,0,0,35,2,11,5,0,0,10,31,8,39,0,0,19,31,13,33] >;

C2×Q16⋊D5 in GAP, Magma, Sage, TeX

C_2\times Q_{16}\rtimes D_5
% in TeX

G:=Group("C2xQ16:D5");
// GroupNames label

G:=SmallGroup(320,1436);
// by ID

G=gap.SmallGroup(320,1436);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,184,1123,185,136,438,235,102,12550]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^8=d^5=e^2=1,c^2=b^4,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,e*b*e=b^5,c*d=d*c,e*c*e=b^4*c,e*d*e=d^-1>;
// generators/relations

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