Copied to
clipboard

G = C2×Dic5⋊D4order 320 = 26·5

Direct product of C2 and Dic5⋊D4

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

Aliases: C2×Dic5⋊D4, C24.59D10, (C2×D4)⋊38D10, Dic58(C2×D4), (C22×D4)⋊8D5, C105(C4⋊D4), (C2×Dic5)⋊22D4, (C22×C10)⋊12D4, C235(C5⋊D4), (D4×C10)⋊57C22, (C23×Dic5)⋊9C2, C22.148(D4×D5), (C2×C20).643C23, (C2×C10).297C24, C10.144(C22×D4), (C22×C4).271D10, C23.D563C22, D10⋊C472C22, C10.D474C22, (C23×C10).77C22, (C23×D5).76C22, C23.338(C22×D5), C22.310(C23×D5), C22.80(D42D5), (C22×C20).438C22, (C22×C10).231C23, (C2×Dic5).294C23, (C22×Dic5)⋊49C22, (C22×D5).128C23, C56(C2×C4⋊D4), (D4×C2×C10)⋊16C2, (C2×C10)⋊9(C2×D4), C2.104(C2×D4×D5), C221(C2×C5⋊D4), C10.106(C2×C4○D4), C2.70(C2×D42D5), (C2×C5⋊D4)⋊46C22, (C22×C5⋊D4)⋊15C2, (C2×C23.D5)⋊29C2, (C2×D10⋊C4)⋊42C2, C2.17(C22×C5⋊D4), (C2×C10.D4)⋊48C2, (C2×C4).237(C22×D5), (C2×C10).178(C4○D4), SmallGroup(320,1474)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C2×Dic5⋊D4
C1C5C10C2×C10C22×D5C23×D5C22×C5⋊D4 — C2×Dic5⋊D4
C5C2×C10 — C2×Dic5⋊D4
C1C23C22×D4

Generators and relations for C2×Dic5⋊D4
 G = < a,b,c,d,e | a2=b10=d4=e2=1, c2=b5, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, dcd-1=b5c, ce=ec, ede=d-1 >

Subgroups: 1486 in 426 conjugacy classes, 135 normal (31 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, C23, C23, C23, D5, C10, C10, C10, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C24, C24, Dic5, Dic5, C20, D10, C2×C10, C2×C10, C2×C10, C2×C22⋊C4, C2×C4⋊C4, C4⋊D4, C23×C4, C22×D4, C22×D4, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×D4, C22×D5, C22×D5, C22×C10, C22×C10, C22×C10, C2×C4⋊D4, C10.D4, D10⋊C4, C23.D5, C22×Dic5, C22×Dic5, C22×Dic5, C2×C5⋊D4, C2×C5⋊D4, C22×C20, D4×C10, D4×C10, C23×D5, C23×C10, C2×C10.D4, C2×D10⋊C4, Dic5⋊D4, C2×C23.D5, C23×Dic5, C22×C5⋊D4, D4×C2×C10, C2×Dic5⋊D4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C4○D4, C24, D10, C4⋊D4, C22×D4, C2×C4○D4, C5⋊D4, C22×D5, C2×C4⋊D4, D4×D5, D42D5, C2×C5⋊D4, C23×D5, Dic5⋊D4, C2×D4×D5, C2×D42D5, C22×C5⋊D4, C2×Dic5⋊D4

Smallest permutation representation of C2×Dic5⋊D4
On 160 points
Generators in S160
(1 107)(2 108)(3 109)(4 110)(5 101)(6 102)(7 103)(8 104)(9 105)(10 106)(11 72)(12 73)(13 74)(14 75)(15 76)(16 77)(17 78)(18 79)(19 80)(20 71)(21 98)(22 99)(23 100)(24 91)(25 92)(26 93)(27 94)(28 95)(29 96)(30 97)(31 124)(32 125)(33 126)(34 127)(35 128)(36 129)(37 130)(38 121)(39 122)(40 123)(41 118)(42 119)(43 120)(44 111)(45 112)(46 113)(47 114)(48 115)(49 116)(50 117)(51 144)(52 145)(53 146)(54 147)(55 148)(56 149)(57 150)(58 141)(59 142)(60 143)(61 138)(62 139)(63 140)(64 131)(65 132)(66 133)(67 134)(68 135)(69 136)(70 137)(81 158)(82 159)(83 160)(84 151)(85 152)(86 153)(87 154)(88 155)(89 156)(90 157)
(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 47 6 42)(2 46 7 41)(3 45 8 50)(4 44 9 49)(5 43 10 48)(11 131 16 136)(12 140 17 135)(13 139 18 134)(14 138 19 133)(15 137 20 132)(21 40 26 35)(22 39 27 34)(23 38 28 33)(24 37 29 32)(25 36 30 31)(51 90 56 85)(52 89 57 84)(53 88 58 83)(54 87 59 82)(55 86 60 81)(61 80 66 75)(62 79 67 74)(63 78 68 73)(64 77 69 72)(65 76 70 71)(91 130 96 125)(92 129 97 124)(93 128 98 123)(94 127 99 122)(95 126 100 121)(101 120 106 115)(102 119 107 114)(103 118 108 113)(104 117 109 112)(105 116 110 111)(141 160 146 155)(142 159 147 154)(143 158 148 153)(144 157 149 152)(145 156 150 151)
(1 87 27 74)(2 88 28 75)(3 89 29 76)(4 90 30 77)(5 81 21 78)(6 82 22 79)(7 83 23 80)(8 84 24 71)(9 85 25 72)(10 86 26 73)(11 105 152 92)(12 106 153 93)(13 107 154 94)(14 108 155 95)(15 109 156 96)(16 110 157 97)(17 101 158 98)(18 102 159 99)(19 103 160 100)(20 104 151 91)(31 64 44 51)(32 65 45 52)(33 66 46 53)(34 67 47 54)(35 68 48 55)(36 69 49 56)(37 70 50 57)(38 61 41 58)(39 62 42 59)(40 63 43 60)(111 144 124 131)(112 145 125 132)(113 146 126 133)(114 147 127 134)(115 148 128 135)(116 149 129 136)(117 150 130 137)(118 141 121 138)(119 142 122 139)(120 143 123 140)
(1 54)(2 55)(3 56)(4 57)(5 58)(6 59)(7 60)(8 51)(9 52)(10 53)(11 125)(12 126)(13 127)(14 128)(15 129)(16 130)(17 121)(18 122)(19 123)(20 124)(21 61)(22 62)(23 63)(24 64)(25 65)(26 66)(27 67)(28 68)(29 69)(30 70)(31 71)(32 72)(33 73)(34 74)(35 75)(36 76)(37 77)(38 78)(39 79)(40 80)(41 81)(42 82)(43 83)(44 84)(45 85)(46 86)(47 87)(48 88)(49 89)(50 90)(91 131)(92 132)(93 133)(94 134)(95 135)(96 136)(97 137)(98 138)(99 139)(100 140)(101 141)(102 142)(103 143)(104 144)(105 145)(106 146)(107 147)(108 148)(109 149)(110 150)(111 151)(112 152)(113 153)(114 154)(115 155)(116 156)(117 157)(118 158)(119 159)(120 160)

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

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

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

68 conjugacy classes

class 1 2A···2G2H2I2J2K2L2M2N2O4A4B4C···4J4K4L5A5B10A···10N10O···10AD20A···20H
order12···222222222444···4445510···1010···1020···20
size11···122224420204410···102020222···24···44···4

68 irreducible representations

dim111111112222222244
type+++++++++++++++-
imageC1C2C2C2C2C2C2C2D4D4D5C4○D4D10D10D10C5⋊D4D4×D5D42D5
kernelC2×Dic5⋊D4C2×C10.D4C2×D10⋊C4Dic5⋊D4C2×C23.D5C23×Dic5C22×C5⋊D4D4×C2×C10C2×Dic5C22×C10C22×D4C2×C10C22×C4C2×D4C24C23C22C22
# reps1118112144242841644

Matrix representation of C2×Dic5⋊D4 in GL6(𝔽41)

100000
010000
0040000
0004000
000010
000001
,
010000
4070000
000100
0040700
000010
000001
,
38380000
1730000
00383800
0017300
0000400
0000040
,
1710000
40240000
0017100
00402400
000001
0000400
,
4000000
0400000
001000
000100
000001
000010

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],[0,40,0,0,0,0,1,7,0,0,0,0,0,0,0,40,0,0,0,0,1,7,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[38,17,0,0,0,0,38,3,0,0,0,0,0,0,38,17,0,0,0,0,38,3,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[17,40,0,0,0,0,1,24,0,0,0,0,0,0,17,40,0,0,0,0,1,24,0,0,0,0,0,0,0,40,0,0,0,0,1,0],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;

C2×Dic5⋊D4 in GAP, Magma, Sage, TeX

C_2\times {\rm Dic}_5\rtimes D_4
% in TeX

G:=Group("C2xDic5:D4");
// GroupNames label

G:=SmallGroup(320,1474);
// by ID

G=gap.SmallGroup(320,1474);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,758,675,297,12550]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^10=d^4=e^2=1,c^2=b^5,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=b^-1,b*d=d*b,b*e=e*b,d*c*d^-1=b^5*c,c*e=e*c,e*d*e=d^-1>;
// generators/relations

׿
×
𝔽