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G = D5×Q8⋊C4order 320 = 26·5

Direct product of D5 and Q8⋊C4

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

Aliases: D5×Q8⋊C4, D10.11Q16, D10.21SD16, (Q8×D5)⋊1C4, Q85(C4×D5), C2.2(D5×Q16), (C4×D5).95D4, C4.162(D4×D5), C2.4(D5×SD16), C4⋊C4.147D10, Q8⋊Dic53C2, C10.Q169C2, (C2×C8).208D10, C20.116(C2×D4), C10.16(C2×Q16), C22.76(D4×D5), Dic1013(C2×C4), C20.47(C22×C4), (C2×Q8).103D10, C10.29(C2×SD16), C20.44D422C2, (C2×C40).196C22, (C2×C20).241C23, (C2×Dic5).138D4, (C22×D5).153D4, C4⋊Dic5.89C22, (Q8×C10).24C22, D10.56(C22⋊C4), Dic5.25(C22⋊C4), (C2×Dic10).72C22, C4.12(C2×C4×D5), (C2×Q8×D5).2C2, (D5×C4⋊C4).1C2, C52(C2×Q8⋊C4), (D5×C2×C8).15C2, (C5×Q8)⋊11(C2×C4), (C4×D5).50(C2×C4), C2.21(D5×C22⋊C4), (C5×Q8⋊C4)⋊18C2, (C2×C10).254(C2×D4), (C5×C4⋊C4).42C22, C10.61(C2×C22⋊C4), (C2×C4×D5).296C22, (C2×C4).348(C22×D5), (C2×C52C8).226C22, SmallGroup(320,428)

Series: Derived Chief Lower central Upper central

C1C20 — D5×Q8⋊C4
C1C5C10C2×C10C2×C20C2×C4×D5C2×Q8×D5 — D5×Q8⋊C4
C5C10C20 — D5×Q8⋊C4
C1C22C2×C4Q8⋊C4

Generators and relations for D5×Q8⋊C4
 G = < a,b,c,d,e | a5=b2=c4=e4=1, d2=c2, bab=a-1, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd-1=ece-1=c-1, ede-1=c-1d >

Subgroups: 606 in 162 conjugacy classes, 63 normal (37 characteristic)
C1, C2 [×3], C2 [×4], C4 [×2], C4 [×8], C22, C22 [×6], C5, C8 [×2], C2×C4, C2×C4 [×15], Q8 [×2], Q8 [×8], C23, D5 [×4], C10 [×3], C4⋊C4, C4⋊C4 [×2], C2×C8, C2×C8 [×3], C22×C4 [×3], C2×Q8, C2×Q8 [×8], Dic5 [×2], Dic5 [×3], C20 [×2], C20 [×3], D10 [×6], C2×C10, Q8⋊C4, Q8⋊C4 [×3], C2×C4⋊C4, C22×C8, C22×Q8, C52C8, C40, Dic10 [×2], Dic10 [×5], C4×D5 [×4], C4×D5 [×6], C2×Dic5, C2×Dic5 [×2], C2×C20, C2×C20 [×2], C5×Q8 [×2], C5×Q8, C22×D5, C2×Q8⋊C4, C8×D5 [×2], C2×C52C8, C10.D4, C4⋊Dic5, C5×C4⋊C4, C2×C40, C2×Dic10, C2×Dic10, C2×C4×D5, C2×C4×D5 [×2], Q8×D5 [×4], Q8×D5 [×2], Q8×C10, C10.Q16, C20.44D4, Q8⋊Dic5, C5×Q8⋊C4, D5×C4⋊C4, D5×C2×C8, C2×Q8×D5, D5×Q8⋊C4
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×4], C23, D5, C22⋊C4 [×4], SD16 [×2], Q16 [×2], C22×C4, C2×D4 [×2], D10 [×3], Q8⋊C4 [×4], C2×C22⋊C4, C2×SD16, C2×Q16, C4×D5 [×2], C22×D5, C2×Q8⋊C4, C2×C4×D5, D4×D5 [×2], D5×C22⋊C4, D5×SD16, D5×Q16, D5×Q8⋊C4

Smallest permutation representation of D5×Q8⋊C4
On 160 points
Generators in S160
(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 28)(2 27)(3 26)(4 30)(5 29)(6 21)(7 25)(8 24)(9 23)(10 22)(11 36)(12 40)(13 39)(14 38)(15 37)(16 31)(17 35)(18 34)(19 33)(20 32)(41 66)(42 70)(43 69)(44 68)(45 67)(46 61)(47 65)(48 64)(49 63)(50 62)(51 76)(52 80)(53 79)(54 78)(55 77)(56 71)(57 75)(58 74)(59 73)(60 72)(81 106)(82 110)(83 109)(84 108)(85 107)(86 101)(87 105)(88 104)(89 103)(90 102)(91 116)(92 120)(93 119)(94 118)(95 117)(96 111)(97 115)(98 114)(99 113)(100 112)(121 146)(122 150)(123 149)(124 148)(125 147)(126 141)(127 145)(128 144)(129 143)(130 142)(131 156)(132 160)(133 159)(134 158)(135 157)(136 151)(137 155)(138 154)(139 153)(140 152)
(1 14 9 19)(2 15 10 20)(3 11 6 16)(4 12 7 17)(5 13 8 18)(21 31 26 36)(22 32 27 37)(23 33 28 38)(24 34 29 39)(25 35 30 40)(41 56 46 51)(42 57 47 52)(43 58 48 53)(44 59 49 54)(45 60 50 55)(61 76 66 71)(62 77 67 72)(63 78 68 73)(64 79 69 74)(65 80 70 75)(81 96 86 91)(82 97 87 92)(83 98 88 93)(84 99 89 94)(85 100 90 95)(101 116 106 111)(102 117 107 112)(103 118 108 113)(104 119 109 114)(105 120 110 115)(121 131 126 136)(122 132 127 137)(123 133 128 138)(124 134 129 139)(125 135 130 140)(141 151 146 156)(142 152 147 157)(143 153 148 158)(144 154 149 159)(145 155 150 160)
(1 109 9 104)(2 110 10 105)(3 106 6 101)(4 107 7 102)(5 108 8 103)(11 116 16 111)(12 117 17 112)(13 118 18 113)(14 119 19 114)(15 120 20 115)(21 86 26 81)(22 87 27 82)(23 88 28 83)(24 89 29 84)(25 90 30 85)(31 96 36 91)(32 97 37 92)(33 98 38 93)(34 99 39 94)(35 100 40 95)(41 146 46 141)(42 147 47 142)(43 148 48 143)(44 149 49 144)(45 150 50 145)(51 156 56 151)(52 157 57 152)(53 158 58 153)(54 159 59 154)(55 160 60 155)(61 126 66 121)(62 127 67 122)(63 128 68 123)(64 129 69 124)(65 130 70 125)(71 136 76 131)(72 137 77 132)(73 138 78 133)(74 139 79 134)(75 140 80 135)
(1 64 24 44)(2 65 25 45)(3 61 21 41)(4 62 22 42)(5 63 23 43)(6 66 26 46)(7 67 27 47)(8 68 28 48)(9 69 29 49)(10 70 30 50)(11 71 31 51)(12 72 32 52)(13 73 33 53)(14 74 34 54)(15 75 35 55)(16 76 36 56)(17 77 37 57)(18 78 38 58)(19 79 39 59)(20 80 40 60)(81 151 101 131)(82 152 102 132)(83 153 103 133)(84 154 104 134)(85 155 105 135)(86 156 106 136)(87 157 107 137)(88 158 108 138)(89 159 109 139)(90 160 110 140)(91 146 111 126)(92 147 112 127)(93 148 113 128)(94 149 114 129)(95 150 115 130)(96 141 116 121)(97 142 117 122)(98 143 118 123)(99 144 119 124)(100 145 120 125)

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

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

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

56 conjugacy classes

class 1 2A2B2C2D2E2F2G4A4B4C4D4E4F4G4H4I4J4K4L5A5B8A8B8C8D8E8F8G8H10A···10F20A20B20C20D20E···20L40A···40H
order12222222444444444444558888888810···102020202020···2040···40
size11115555224444101020202020222222101010102···244448···84···4

56 irreducible representations

dim11111111122222222224444
type++++++++++++-+++++-
imageC1C2C2C2C2C2C2C2C4D4D4D4D5SD16Q16D10D10D10C4×D5D4×D5D4×D5D5×SD16D5×Q16
kernelD5×Q8⋊C4C10.Q16C20.44D4Q8⋊Dic5C5×Q8⋊C4D5×C4⋊C4D5×C2×C8C2×Q8×D5Q8×D5C4×D5C2×Dic5C22×D5Q8⋊C4D10D10C4⋊C4C2×C8C2×Q8Q8C4C22C2C2
# reps11111111821124422282244

Matrix representation of D5×Q8⋊C4 in GL5(𝔽41)

10000
01000
00100
00001
000406
,
10000
040000
004000
00001
00010
,
10000
004000
01000
00010
00001
,
10000
0353900
039600
000400
000040
,
90000
0193800
0382200
000400
000040

G:=sub<GL(5,GF(41))| [1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,1,6],[1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,1,0],[1,0,0,0,0,0,0,1,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,35,39,0,0,0,39,6,0,0,0,0,0,40,0,0,0,0,0,40],[9,0,0,0,0,0,19,38,0,0,0,38,22,0,0,0,0,0,40,0,0,0,0,0,40] >;

D5×Q8⋊C4 in GAP, Magma, Sage, TeX

D_5\times Q_8\rtimes C_4
% in TeX

G:=Group("D5xQ8:C4");
// GroupNames label

G:=SmallGroup(320,428);
// by ID

G=gap.SmallGroup(320,428);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,219,58,851,438,102,12550]);
// Polycyclic

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

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