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G = C23.47D20order 320 = 26·5

18th non-split extension by C23 of D20 acting via D20/D10=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C23.47D20, M4(2)⋊1Dic5, C4013(C2×C4), C406C43C2, C81(C2×Dic5), C405C417C2, (C2×C8).75D10, C20.52(C4⋊C4), C20.76(C2×Q8), (C2×C20).26Q8, (C2×C20).167D4, (C2×C4).149D20, (C5×M4(2))⋊7C4, C4.6(C4⋊Dic5), C2.3(C8⋊D10), (C2×C40).61C22, C4.42(C2×Dic10), (C2×C4).15Dic10, C22.56(C2×D20), (C2×M4(2)).1D5, C10.19(C8⋊C22), C56(M4(2)⋊C4), (C2×C20).772C23, C20.232(C22×C4), C2.4(C8.D10), (C22×C10).100D4, (C22×C4).133D10, (C10×M4(2)).1C2, C22.6(C4⋊Dic5), C4.27(C22×Dic5), C10.20(C8.C22), C4⋊Dic5.284C22, (C22×C20).180C22, C23.21D10.17C2, C10.73(C2×C4⋊C4), C2.14(C2×C4⋊Dic5), (C2×C10).44(C4⋊C4), (C2×C20).273(C2×C4), (C2×C10).162(C2×D4), (C2×C4⋊Dic5).40C2, (C2×C4).21(C2×Dic5), (C2×C4).720(C22×D5), SmallGroup(320,748)

Series: Derived Chief Lower central Upper central

C1C20 — C23.47D20
C1C5C10C2×C10C2×C20C4⋊Dic5C2×C4⋊Dic5 — C23.47D20
C5C10C20 — C23.47D20
C1C22C22×C4C2×M4(2)

Generators and relations for C23.47D20
 G = < a,b,c,d,e | a2=b2=c2=1, d20=c, e2=cb=bc, ab=ba, dad-1=eae-1=ac=ca, bd=db, be=eb, cd=dc, ce=ec, ede-1=d19 >

Subgroups: 382 in 118 conjugacy classes, 71 normal (29 characteristic)
C1, C2 [×3], C2 [×2], C4 [×2], C4 [×2], C4 [×4], C22, C22 [×2], C22 [×2], C5, C8 [×4], C2×C4 [×2], C2×C4 [×4], C2×C4 [×6], C23, C10 [×3], C10 [×2], C42, C22⋊C4, C4⋊C4 [×5], C2×C8 [×2], M4(2) [×4], C22×C4, C22×C4, Dic5 [×4], C20 [×2], C20 [×2], C2×C10, C2×C10 [×2], C2×C10 [×2], C4.Q8 [×2], C2.D8 [×2], C2×C4⋊C4, C42⋊C2, C2×M4(2), C40 [×4], C2×Dic5 [×6], C2×C20 [×2], C2×C20 [×4], C22×C10, M4(2)⋊C4, C4×Dic5, C4⋊Dic5 [×2], C4⋊Dic5 [×2], C4⋊Dic5, C23.D5, C2×C40 [×2], C5×M4(2) [×4], C22×Dic5, C22×C20, C406C4 [×2], C405C4 [×2], C2×C4⋊Dic5, C23.21D10, C10×M4(2), C23.47D20
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×2], Q8 [×2], C23, D5, C4⋊C4 [×4], C22×C4, C2×D4, C2×Q8, Dic5 [×4], D10 [×3], C2×C4⋊C4, C8⋊C22, C8.C22, Dic10 [×2], D20 [×2], C2×Dic5 [×6], C22×D5, M4(2)⋊C4, C4⋊Dic5 [×4], C2×Dic10, C2×D20, C22×Dic5, C8⋊D10, C8.D10, C2×C4⋊Dic5, C23.47D20

Smallest permutation representation of C23.47D20
On 160 points
Generators in S160
(1 99)(2 120)(3 101)(4 82)(5 103)(6 84)(7 105)(8 86)(9 107)(10 88)(11 109)(12 90)(13 111)(14 92)(15 113)(16 94)(17 115)(18 96)(19 117)(20 98)(21 119)(22 100)(23 81)(24 102)(25 83)(26 104)(27 85)(28 106)(29 87)(30 108)(31 89)(32 110)(33 91)(34 112)(35 93)(36 114)(37 95)(38 116)(39 97)(40 118)(41 123)(42 144)(43 125)(44 146)(45 127)(46 148)(47 129)(48 150)(49 131)(50 152)(51 133)(52 154)(53 135)(54 156)(55 137)(56 158)(57 139)(58 160)(59 141)(60 122)(61 143)(62 124)(63 145)(64 126)(65 147)(66 128)(67 149)(68 130)(69 151)(70 132)(71 153)(72 134)(73 155)(74 136)(75 157)(76 138)(77 159)(78 140)(79 121)(80 142)
(1 99)(2 100)(3 101)(4 102)(5 103)(6 104)(7 105)(8 106)(9 107)(10 108)(11 109)(12 110)(13 111)(14 112)(15 113)(16 114)(17 115)(18 116)(19 117)(20 118)(21 119)(22 120)(23 81)(24 82)(25 83)(26 84)(27 85)(28 86)(29 87)(30 88)(31 89)(32 90)(33 91)(34 92)(35 93)(36 94)(37 95)(38 96)(39 97)(40 98)(41 143)(42 144)(43 145)(44 146)(45 147)(46 148)(47 149)(48 150)(49 151)(50 152)(51 153)(52 154)(53 155)(54 156)(55 157)(56 158)(57 159)(58 160)(59 121)(60 122)(61 123)(62 124)(63 125)(64 126)(65 127)(66 128)(67 129)(68 130)(69 131)(70 132)(71 133)(72 134)(73 135)(74 136)(75 137)(76 138)(77 139)(78 140)(79 141)(80 142)
(1 21)(2 22)(3 23)(4 24)(5 25)(6 26)(7 27)(8 28)(9 29)(10 30)(11 31)(12 32)(13 33)(14 34)(15 35)(16 36)(17 37)(18 38)(19 39)(20 40)(41 61)(42 62)(43 63)(44 64)(45 65)(46 66)(47 67)(48 68)(49 69)(50 70)(51 71)(52 72)(53 73)(54 74)(55 75)(56 76)(57 77)(58 78)(59 79)(60 80)(81 101)(82 102)(83 103)(84 104)(85 105)(86 106)(87 107)(88 108)(89 109)(90 110)(91 111)(92 112)(93 113)(94 114)(95 115)(96 116)(97 117)(98 118)(99 119)(100 120)(121 141)(122 142)(123 143)(124 144)(125 145)(126 146)(127 147)(128 148)(129 149)(130 150)(131 151)(132 152)(133 153)(134 154)(135 155)(136 156)(137 157)(138 158)(139 159)(140 160)
(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 43 119 125)(2 62 120 144)(3 41 81 123)(4 60 82 142)(5 79 83 121)(6 58 84 140)(7 77 85 159)(8 56 86 138)(9 75 87 157)(10 54 88 136)(11 73 89 155)(12 52 90 134)(13 71 91 153)(14 50 92 132)(15 69 93 151)(16 48 94 130)(17 67 95 149)(18 46 96 128)(19 65 97 147)(20 44 98 126)(21 63 99 145)(22 42 100 124)(23 61 101 143)(24 80 102 122)(25 59 103 141)(26 78 104 160)(27 57 105 139)(28 76 106 158)(29 55 107 137)(30 74 108 156)(31 53 109 135)(32 72 110 154)(33 51 111 133)(34 70 112 152)(35 49 113 131)(36 68 114 150)(37 47 115 129)(38 66 116 148)(39 45 117 127)(40 64 118 146)

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

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

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

62 conjugacy classes

class 1 2A2B2C2D2E4A4B4C4D4E···4L5A5B8A8B8C8D10A···10F10G10H10I10J20A···20H20I20J20K20L40A···40P
order12222244444···455888810···101010101020···202020202040···40
size111122222220···202244442···244442···244444···4

62 irreducible representations

dim111111122222222224444
type+++++++-+++-+-+++-+-
imageC1C2C2C2C2C2C4D4Q8D4D5D10Dic5D10Dic10D20D20C8⋊C22C8.C22C8⋊D10C8.D10
kernelC23.47D20C406C4C405C4C2×C4⋊Dic5C23.21D10C10×M4(2)C5×M4(2)C2×C20C2×C20C22×C10C2×M4(2)C2×C8M4(2)C22×C4C2×C4C2×C4C23C10C10C2C2
# reps122111812124828441144

Matrix representation of C23.47D20 in GL6(𝔽41)

100000
010000
0040000
0004000
000010
000001
,
4000000
0400000
0040000
0004000
0000400
0000040
,
100000
010000
0040000
0004000
0000400
0000040
,
1400000
3660000
000010
000001
00403900
001100
,
3290000
090000
0000236
00002118
00183500
00202300

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],[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],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,36,0,0,0,0,40,6,0,0,0,0,0,0,0,0,40,1,0,0,0,0,39,1,0,0,1,0,0,0,0,0,0,1,0,0],[32,0,0,0,0,0,9,9,0,0,0,0,0,0,0,0,18,20,0,0,0,0,35,23,0,0,23,21,0,0,0,0,6,18,0,0] >;

C23.47D20 in GAP, Magma, Sage, TeX

C_2^3._{47}D_{20}
% in TeX

G:=Group("C2^3.47D20");
// GroupNames label

G:=SmallGroup(320,748);
// by ID

G=gap.SmallGroup(320,748);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,56,422,387,100,1684,102,12550]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^2=1,d^20=c,e^2=c*b=b*c,a*b=b*a,d*a*d^-1=e*a*e^-1=a*c=c*a,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^19>;
// generators/relations

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