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G = C2×SD16⋊D5order 320 = 26·5

Direct product of C2 and SD16⋊D5

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

Aliases: C2×SD16⋊D5, SD169D10, C20.7C24, C40.35C23, Dic2017C22, Dic10.3C23, C4.44(D4×D5), (C2×SD16)⋊5D5, (C4×D5).16D4, C20.82(C2×D4), (Q8×D5)⋊6C22, C4.7(C23×D5), (C10×SD16)⋊6C2, D10.85(C2×D4), (C2×C8).103D10, C8⋊D59C22, C52C8.2C23, C5⋊Q166C22, D4.5(C22×D5), (C5×D4).5C23, (C4×D5).4C23, C8.11(C22×D5), (C2×Dic20)⋊26C2, (C2×D4).183D10, Q8.1(C22×D5), (C5×Q8).1C23, C102(C8.C22), D4.D510C22, (C2×Q8).150D10, Dic5.96(C2×D4), (C5×SD16)⋊9C22, C22.140(D4×D5), (C2×C20).524C23, (C2×C40).117C22, (C2×Dic5).249D4, D42D5.8C22, (C22×D5).136D4, C10.108(C22×D4), (D4×C10).165C22, (Q8×C10).147C22, (C2×Dic10).202C22, (C2×Q8×D5)⋊15C2, C2.81(C2×D4×D5), C52(C2×C8.C22), (C2×C8⋊D5)⋊5C2, (C2×D4.D5)⋊28C2, (C2×C5⋊Q16)⋊25C2, (C2×C10).397(C2×D4), (C2×C4×D5).166C22, (C2×D42D5).12C2, (C2×C4).613(C22×D5), (C2×C52C8).180C22, SmallGroup(320,1432)

Series: Derived Chief Lower central Upper central

C1C20 — C2×SD16⋊D5
C1C5C10C20C4×D5C2×C4×D5C2×Q8×D5 — C2×SD16⋊D5
C5C10C20 — C2×SD16⋊D5
C1C22C2×C4C2×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, C2, C4, C4, C22, C22, C5, C8, C8, C2×C4, C2×C4, D4, D4, Q8, Q8, C23, D5, C10, C10, C10, C2×C8, C2×C8, M4(2), SD16, SD16, Q16, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic5, Dic5, C20, C20, D10, D10, C2×C10, C2×C10, C2×M4(2), C2×SD16, C2×SD16, C2×Q16, C8.C22, C22×Q8, C2×C4○D4, C52C8, C40, Dic10, Dic10, C4×D5, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×D4, C5×D4, C5×Q8, C5×Q8, C22×D5, C22×C10, C2×C8.C22, C8⋊D5, Dic20, C2×C52C8, D4.D5, C5⋊Q16, C2×C40, C5×SD16, C2×Dic10, C2×Dic10, C2×C4×D5, C2×C4×D5, D42D5, D42D5, Q8×D5, Q8×D5, C22×Dic5, C2×C5⋊D4, D4×C10, Q8×C10, C2×C8⋊D5, C2×Dic20, SD16⋊D5, C2×D4.D5, C2×C5⋊Q16, C10×SD16, C2×D42D5, C2×Q8×D5, C2×SD16⋊D5
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C24, D10, C8.C22, C22×D4, C22×D5, C2×C8.C22, D4×D5, C23×D5, SD16⋊D5, C2×D4×D5, C2×SD16⋊D5

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

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

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

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

50 conjugacy classes

class 1 2A2B2C2D2E2F2G4A4B4C4D4E4F4G4H4I4J5A5B8A8B8C8D10A···10F10G10H10I10J20A20B20C20D20E20F20G20H40A···40H
order12222222444444444455888810···1010101010202020202020202040···40
size11114410102244101020202020224420202···28888444488884···4

50 irreducible representations

dim111111111222222224444
type+++++++++++++++++-++-
imageC1C2C2C2C2C2C2C2C2D4D4D4D5D10D10D10D10C8.C22D4×D5D4×D5SD16⋊D5
kernelC2×SD16⋊D5C2×C8⋊D5C2×Dic20SD16⋊D5C2×D4.D5C2×C5⋊Q16C10×SD16C2×D42D5C2×Q8×D5C4×D5C2×Dic5C22×D5C2×SD16C2×C8SD16C2×D4C2×Q8C10C4C22C2
# reps111811111211228222228

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

4000000
0400000
0040000
0004000
0000400
0000040
,
11300000
26300000
007253416
001634257
00243300
0081700
,
4040000
010000
0036293928
00125132
00352512
003962936
,
100000
010000
0064000
001000
0000640
000010
,
4000000
0400000
0064000
00353500
0000640
00003535

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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