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G = C22⋊C8⋊D5order 320 = 26·5

12nd semidirect product of C22⋊C8 and D5 acting via D5/C5=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C22⋊C812D5, C4.196(D4×D5), (C2×D20).19C4, (C4×D5).103D4, (C2×C8).163D10, C20.355(C2×D4), D101C818C2, C23.12(C4×D5), C10.32(C8○D4), C20.55D42C2, (C22×C4).78D10, (C2×C20).822C23, (C2×C40).171C22, (C2×Dic10).20C4, D10.20(C22⋊C4), (C22×C20).93C22, C2.10(D20.2C4), C2.10(D20.3C4), Dic5.19(C22⋊C4), (D5×C2×C8)⋊14C2, (C2×C4).31(C4×D5), (C2×C8⋊D5)⋊12C2, (C5×C22⋊C8)⋊16C2, (C2×C4○D20).1C2, (C2×C5⋊D4).13C4, C2.10(D5×C22⋊C4), C22.104(C2×C4×D5), (C2×C20).212(C2×C4), C54((C22×C8)⋊C2), C10.50(C2×C22⋊C4), (C2×C4×D5).344C22, (C2×Dic5).95(C2×C4), (C22×D5).17(C2×C4), (C2×C4).764(C22×D5), (C2×C10).178(C22×C4), (C22×C10).108(C2×C4), (C2×C52C8).309C22, SmallGroup(320,354)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C22⋊C8⋊D5
C1C5C10C20C2×C20C2×C4×D5C2×C4○D20 — C22⋊C8⋊D5
C5C2×C10 — C22⋊C8⋊D5
C1C2×C4C22⋊C8

Generators and relations for C22⋊C8⋊D5
 G = < a,b,c,d,e | a2=b2=c8=d5=e2=1, cac-1=ab=ba, ad=da, eae=ac4, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede=d-1 >

Subgroups: 590 in 158 conjugacy classes, 55 normal (47 characteristic)
C1, C2 [×3], C2 [×4], C4 [×2], C4 [×4], C22, C22 [×10], C5, C8 [×4], C2×C4 [×2], C2×C4 [×10], D4 [×6], Q8 [×2], C23, C23 [×2], D5 [×3], C10 [×3], C10, C2×C8 [×2], C2×C8 [×4], M4(2) [×2], C22×C4, C22×C4 [×2], C2×D4 [×3], C2×Q8, C4○D4 [×4], Dic5 [×2], Dic5, C20 [×2], C20, D10 [×2], D10 [×5], C2×C10, C2×C10 [×3], C22⋊C8, C22⋊C8 [×3], C22×C8, C2×M4(2), C2×C4○D4, C52C8 [×2], C40 [×2], Dic10 [×2], C4×D5 [×4], C4×D5 [×2], D20 [×2], C2×Dic5 [×2], C5⋊D4 [×4], C2×C20 [×2], C2×C20 [×2], C22×D5 [×2], C22×C10, (C22×C8)⋊C2, C8×D5 [×2], C8⋊D5 [×2], C2×C52C8 [×2], C2×C40 [×2], C2×Dic10, C2×C4×D5 [×2], C2×D20, C4○D20 [×4], C2×C5⋊D4 [×2], C22×C20, D101C8 [×2], C20.55D4, C5×C22⋊C8, D5×C2×C8, C2×C8⋊D5, C2×C4○D20, C22⋊C8⋊D5
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×4], C23, D5, C22⋊C4 [×4], C22×C4, C2×D4 [×2], D10 [×3], C2×C22⋊C4, C8○D4 [×2], C4×D5 [×2], C22×D5, (C22×C8)⋊C2, C2×C4×D5, D4×D5 [×2], D5×C22⋊C4, D20.3C4, D20.2C4, C22⋊C8⋊D5

Smallest permutation representation of C22⋊C8⋊D5
On 160 points
Generators in S160
(1 47)(2 91)(3 41)(4 93)(5 43)(6 95)(7 45)(8 89)(9 22)(10 136)(11 24)(12 130)(13 18)(14 132)(15 20)(16 134)(17 124)(19 126)(21 128)(23 122)(25 50)(26 148)(27 52)(28 150)(29 54)(30 152)(31 56)(32 146)(33 60)(34 139)(35 62)(36 141)(37 64)(38 143)(39 58)(40 137)(42 114)(44 116)(46 118)(48 120)(49 107)(51 109)(53 111)(55 105)(57 102)(59 104)(61 98)(63 100)(65 77)(66 81)(67 79)(68 83)(69 73)(70 85)(71 75)(72 87)(74 155)(76 157)(78 159)(80 153)(82 160)(84 154)(86 156)(88 158)(90 119)(92 113)(94 115)(96 117)(97 138)(99 140)(101 142)(103 144)(106 145)(108 147)(110 149)(112 151)(121 135)(123 129)(125 131)(127 133)
(1 119)(2 120)(3 113)(4 114)(5 115)(6 116)(7 117)(8 118)(9 121)(10 122)(11 123)(12 124)(13 125)(14 126)(15 127)(16 128)(17 130)(18 131)(19 132)(20 133)(21 134)(22 135)(23 136)(24 129)(25 108)(26 109)(27 110)(28 111)(29 112)(30 105)(31 106)(32 107)(33 97)(34 98)(35 99)(36 100)(37 101)(38 102)(39 103)(40 104)(41 92)(42 93)(43 94)(44 95)(45 96)(46 89)(47 90)(48 91)(49 146)(50 147)(51 148)(52 149)(53 150)(54 151)(55 152)(56 145)(57 143)(58 144)(59 137)(60 138)(61 139)(62 140)(63 141)(64 142)(65 158)(66 159)(67 160)(68 153)(69 154)(70 155)(71 156)(72 157)(73 84)(74 85)(75 86)(76 87)(77 88)(78 81)(79 82)(80 83)
(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 73 97 121 50)(2 74 98 122 51)(3 75 99 123 52)(4 76 100 124 53)(5 77 101 125 54)(6 78 102 126 55)(7 79 103 127 56)(8 80 104 128 49)(9 147 119 84 33)(10 148 120 85 34)(11 149 113 86 35)(12 150 114 87 36)(13 151 115 88 37)(14 152 116 81 38)(15 145 117 82 39)(16 146 118 83 40)(17 111 93 157 63)(18 112 94 158 64)(19 105 95 159 57)(20 106 96 160 58)(21 107 89 153 59)(22 108 90 154 60)(23 109 91 155 61)(24 110 92 156 62)(25 47 69 138 135)(26 48 70 139 136)(27 41 71 140 129)(28 42 72 141 130)(29 43 65 142 131)(30 44 66 143 132)(31 45 67 144 133)(32 46 68 137 134)
(1 27)(2 28)(3 29)(4 30)(5 31)(6 32)(7 25)(8 26)(9 156)(10 157)(11 158)(12 159)(13 160)(14 153)(15 154)(16 155)(17 85)(18 86)(19 87)(20 88)(21 81)(22 82)(23 83)(24 84)(33 62)(34 63)(35 64)(36 57)(37 58)(38 59)(39 60)(40 61)(41 50)(42 51)(43 52)(44 53)(45 54)(46 55)(47 56)(48 49)(65 123)(66 124)(67 125)(68 126)(69 127)(70 128)(71 121)(72 122)(73 129)(74 130)(75 131)(76 132)(77 133)(78 134)(79 135)(80 136)(89 152)(90 145)(91 146)(92 147)(93 148)(94 149)(95 150)(96 151)(97 140)(98 141)(99 142)(100 143)(101 144)(102 137)(103 138)(104 139)(105 114)(106 115)(107 116)(108 117)(109 118)(110 119)(111 120)(112 113)

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

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

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

68 conjugacy classes

class 1 2A2B2C2D2E2F2G4A4B4C4D4E4F4G4H5A5B8A8B8C8D8E8F8G8H8I8J8K8L10A···10F10G10H10I10J20A···20H20I20J20K20L40A···40P
order12222222444444445588888888888810···101010101020···202020202040···40
size1111410102011114101020222222441010101020202···244442···244444···4

68 irreducible representations

dim11111111112222222244
type++++++++++++
imageC1C2C2C2C2C2C2C4C4C4D4D5D10D10C8○D4C4×D5C4×D5D20.3C4D4×D5D20.2C4
kernelC22⋊C8⋊D5D101C8C20.55D4C5×C22⋊C8D5×C2×C8C2×C8⋊D5C2×C4○D20C2×Dic10C2×D20C2×C5⋊D4C4×D5C22⋊C8C2×C8C22×C4C10C2×C4C23C2C4C2
# reps121111122442428441644

Matrix representation of C22⋊C8⋊D5 in GL4(𝔽41) generated by

22600
221900
001835
00623
,
40000
04000
0010
0001
,
162300
172500
00380
00038
,
1000
0100
0001
00406
,
341300
31700
002839
00213
G:=sub<GL(4,GF(41))| [22,22,0,0,6,19,0,0,0,0,18,6,0,0,35,23],[40,0,0,0,0,40,0,0,0,0,1,0,0,0,0,1],[16,17,0,0,23,25,0,0,0,0,38,0,0,0,0,38],[1,0,0,0,0,1,0,0,0,0,0,40,0,0,1,6],[34,31,0,0,13,7,0,0,0,0,28,2,0,0,39,13] >;

C22⋊C8⋊D5 in GAP, Magma, Sage, TeX

C_2^2\rtimes C_8\rtimes D_5
% in TeX

G:=Group("C2^2:C8:D5");
// GroupNames label

G:=SmallGroup(320,354);
// by ID

G=gap.SmallGroup(320,354);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,477,219,58,136,12550]);
// Polycyclic

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

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