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## G = C2×SD16⋊D5order 320 = 26·5

### Direct product of C2 and SD16⋊D5

Series: Derived Chief Lower central Upper central

 Derived series C1 — C20 — C2×SD16⋊D5
 Chief series C1 — C5 — C10 — C20 — C4×D5 — C2×C4×D5 — C2×Q8×D5 — C2×SD16⋊D5
 Lower central C5 — C10 — C20 — C2×SD16⋊D5
 Upper central C1 — C22 — C2×C4 — C2×SD16

Generators and relations for C2×SD16⋊D5
G = < a,b,c,d,e | a2=b8=c2=d5=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=b3, bd=db, ebe=b5, cd=dc, ece=b4c, ede=d-1 >

Subgroups: 894 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 [×2], D4 [×5], Q8 [×2], Q8 [×11], C23 [×2], D5 [×2], C10, C10 [×2], C10 [×2], C2×C8, C2×C8, M4(2) [×4], SD16 [×4], SD16 [×4], Q16 [×8], C22×C4 [×3], C2×D4, C2×D4, C2×Q8, C2×Q8 [×9], C4○D4 [×6], Dic5 [×2], Dic5 [×4], C20 [×2], C20 [×2], D10 [×2], D10 [×2], C2×C10, C2×C10 [×4], C2×M4(2), C2×SD16, C2×SD16, C2×Q16 [×2], C8.C22 [×8], C22×Q8, C2×C4○D4, C52C8 [×2], C40 [×2], Dic10 [×4], Dic10 [×6], C4×D5 [×4], C4×D5 [×4], C2×Dic5, C2×Dic5 [×6], C5⋊D4 [×4], C2×C20, C2×C20, C5×D4 [×2], C5×D4, C5×Q8 [×2], C5×Q8, C22×D5, C22×C10, C2×C8.C22, C8⋊D5 [×4], Dic20 [×4], C2×C52C8, D4.D5 [×4], C5⋊Q16 [×4], C2×C40, C5×SD16 [×4], C2×Dic10 [×2], C2×Dic10, C2×C4×D5, C2×C4×D5, D42D5 [×4], D42D5 [×2], Q8×D5 [×4], Q8×D5 [×2], C22×Dic5, C2×C5⋊D4, D4×C10, Q8×C10, C2×C8⋊D5, C2×Dic20, SD16⋊D5 [×8], C2×D4.D5, C2×C5⋊Q16, C10×SD16, C2×D42D5, C2×Q8×D5, C2×SD16⋊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, SD16⋊D5 [×2], C2×D4×D5, C2×SD16⋊D5

Smallest permutation representation of C2×SD16⋊D5
On 160 points
Generators in S160
(1 102)(2 103)(3 104)(4 97)(5 98)(6 99)(7 100)(8 101)(9 124)(10 125)(11 126)(12 127)(13 128)(14 121)(15 122)(16 123)(17 157)(18 158)(19 159)(20 160)(21 153)(22 154)(23 155)(24 156)(25 84)(26 85)(27 86)(28 87)(29 88)(30 81)(31 82)(32 83)(33 137)(34 138)(35 139)(36 140)(37 141)(38 142)(39 143)(40 144)(41 148)(42 149)(43 150)(44 151)(45 152)(46 145)(47 146)(48 147)(49 91)(50 92)(51 93)(52 94)(53 95)(54 96)(55 89)(56 90)(57 110)(58 111)(59 112)(60 105)(61 106)(62 107)(63 108)(64 109)(65 135)(66 136)(67 129)(68 130)(69 131)(70 132)(71 133)(72 134)(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)(2 80)(3 75)(4 78)(5 73)(6 76)(7 79)(8 74)(9 47)(10 42)(11 45)(12 48)(13 43)(14 46)(15 41)(16 44)(17 140)(18 143)(19 138)(20 141)(21 144)(22 139)(23 142)(24 137)(25 61)(26 64)(27 59)(28 62)(29 57)(30 60)(31 63)(32 58)(33 156)(34 159)(35 154)(36 157)(37 160)(38 155)(39 158)(40 153)(49 72)(50 67)(51 70)(52 65)(53 68)(54 71)(55 66)(56 69)(81 105)(82 108)(83 111)(84 106)(85 109)(86 112)(87 107)(88 110)(89 136)(90 131)(91 134)(92 129)(93 132)(94 135)(95 130)(96 133)(97 118)(98 113)(99 116)(100 119)(101 114)(102 117)(103 120)(104 115)(121 145)(122 148)(123 151)(124 146)(125 149)(126 152)(127 147)(128 150)
(1 127 34 109 133)(2 128 35 110 134)(3 121 36 111 135)(4 122 37 112 136)(5 123 38 105 129)(6 124 39 106 130)(7 125 40 107 131)(8 126 33 108 132)(9 143 61 68 99)(10 144 62 69 100)(11 137 63 70 101)(12 138 64 71 102)(13 139 57 72 103)(14 140 58 65 104)(15 141 59 66 97)(16 142 60 67 98)(17 32 52 115 46)(18 25 53 116 47)(19 26 54 117 48)(20 27 55 118 41)(21 28 56 119 42)(22 29 49 120 43)(23 30 50 113 44)(24 31 51 114 45)(73 151 155 81 92)(74 152 156 82 93)(75 145 157 83 94)(76 146 158 84 95)(77 147 159 85 96)(78 148 160 86 89)(79 149 153 87 90)(80 150 154 88 91)
(1 133)(2 130)(3 135)(4 132)(5 129)(6 134)(7 131)(8 136)(9 57)(10 62)(11 59)(12 64)(13 61)(14 58)(15 63)(16 60)(17 21)(19 23)(25 47)(26 44)(27 41)(28 46)(29 43)(30 48)(31 45)(32 42)(33 37)(35 39)(49 120)(50 117)(51 114)(52 119)(53 116)(54 113)(55 118)(56 115)(65 104)(66 101)(67 98)(68 103)(69 100)(70 97)(71 102)(72 99)(73 96)(74 93)(75 90)(76 95)(77 92)(78 89)(79 94)(80 91)(81 147)(82 152)(83 149)(84 146)(85 151)(86 148)(87 145)(88 150)(105 123)(106 128)(107 125)(108 122)(109 127)(110 124)(111 121)(112 126)(137 141)(139 143)(153 157)(155 159)

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

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

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

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 10G 10H 10I 10J 20A 20B 20C 20D 20E 20F 20G 20H 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 10 10 10 10 20 20 20 20 20 20 20 20 40 ··· 40 size 1 1 1 1 4 4 10 10 2 2 4 4 10 10 20 20 20 20 2 2 4 4 20 20 2 ··· 2 8 8 8 8 4 4 4 4 8 8 8 8 4 ··· 4

50 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 2 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 D10 C8.C22 D4×D5 D4×D5 SD16⋊D5 kernel C2×SD16⋊D5 C2×C8⋊D5 C2×Dic20 SD16⋊D5 C2×D4.D5 C2×C5⋊Q16 C10×SD16 C2×D4⋊2D5 C2×Q8×D5 C4×D5 C2×Dic5 C22×D5 C2×SD16 C2×C8 SD16 C2×D4 C2×Q8 C10 C4 C22 C2 # reps 1 1 1 8 1 1 1 1 1 2 1 1 2 2 8 2 2 2 2 2 8

Matrix representation of C2×SD16⋊D5 in GL6(𝔽41)

 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40
,
 11 30 0 0 0 0 26 30 0 0 0 0 0 0 7 25 34 16 0 0 16 34 25 7 0 0 24 33 0 0 0 0 8 17 0 0
,
 40 4 0 0 0 0 0 1 0 0 0 0 0 0 36 29 39 28 0 0 12 5 13 2 0 0 35 2 5 12 0 0 39 6 29 36
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 6 40 0 0 0 0 1 0 0 0 0 0 0 0 6 40 0 0 0 0 1 0
,
 40 0 0 0 0 0 0 40 0 0 0 0 0 0 6 40 0 0 0 0 35 35 0 0 0 0 0 0 6 40 0 0 0 0 35 35

G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[11,26,0,0,0,0,30,30,0,0,0,0,0,0,7,16,24,8,0,0,25,34,33,17,0,0,34,25,0,0,0,0,16,7,0,0],[40,0,0,0,0,0,4,1,0,0,0,0,0,0,36,12,35,39,0,0,29,5,2,6,0,0,39,13,5,29,0,0,28,2,12,36],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,6,1,0,0,0,0,40,0,0,0,0,0,0,0,6,1,0,0,0,0,40,0],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,6,35,0,0,0,0,40,35,0,0,0,0,0,0,6,35,0,0,0,0,40,35] >;

C2×SD16⋊D5 in GAP, Magma, Sage, TeX

C_2\times {\rm SD}_{16}\rtimes D_5
% in TeX

G:=Group("C2xSD16:D5");
// GroupNames label

G:=SmallGroup(320,1432);
// by ID

G=gap.SmallGroup(320,1432);
# by ID

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

G:=Group<a,b,c,d,e|a^2=b^8=c^2=d^5=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^3,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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