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G = C10.362+ 1+4order 320 = 26·5

36th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.362+ 1+4, C10.712- 1+4, C20⋊Q819C2, C4⋊D4.9D5, C4⋊C4.179D10, (D4×Dic5)⋊19C2, (C2×D4).91D10, C22⋊C4.7D10, (C2×C20).37C23, Dic53Q822C2, C20.202(C4○D4), C20.17D416C2, C4.68(D42D5), C20.48D432C2, (C2×C10).147C24, (C22×C4).222D10, C2.38(D46D10), C23.13(C22×D5), (D4×C10).121C22, C23.D1017C2, C23.18D108C2, C4⋊Dic5.310C22, (C2×Dic5).68C23, C22.168(C23×D5), Dic5.14D418C2, C23.D5.24C22, C23.21D1025C2, (C22×C20).239C22, (C22×C10).185C23, C54(C22.36C24), (C4×Dic5).102C22, C10.D4.17C22, C2.29(D4.10D10), (C2×Dic10).159C22, (C22×Dic5).108C22, C10.83(C2×C4○D4), (C5×C4⋊D4).9C2, C2.35(C2×D42D5), (C2×C4).36(C22×D5), (C5×C4⋊C4).143C22, (C5×C22⋊C4).12C22, SmallGroup(320,1275)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C10.362+ 1+4
C1C5C10C2×C10C2×Dic5C22×Dic5D4×Dic5 — C10.362+ 1+4
C5C2×C10 — C10.362+ 1+4
C1C22C4⋊D4

Generators and relations for C10.362+ 1+4
 G = < a,b,c,d,e | a10=b4=c2=1, d2=e2=a5b2, bab-1=dad-1=a-1, ac=ca, ae=ea, cbc=a5b-1, dbd-1=a5b, be=eb, dcd-1=a5c, ce=ec, ede-1=a5b2d >

Subgroups: 670 in 216 conjugacy classes, 95 normal (43 characteristic)
C1, C2 [×3], C2 [×3], C4 [×2], C4 [×11], C22, C22 [×9], C5, C2×C4 [×2], C2×C4 [×2], C2×C4 [×12], D4 [×4], Q8 [×4], C23, C23 [×2], C10 [×3], C10 [×3], C42 [×4], C22⋊C4 [×2], C22⋊C4 [×10], C4⋊C4, C4⋊C4 [×9], C22×C4, C22×C4 [×2], C2×D4, C2×D4 [×2], C2×Q8 [×3], Dic5 [×8], C20 [×2], C20 [×3], C2×C10, C2×C10 [×9], C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8 [×3], C22.D4 [×2], C4.4D4 [×3], C422C2 [×2], C4⋊Q8, Dic10 [×4], C2×Dic5 [×4], C2×Dic5 [×4], C2×Dic5 [×2], C2×C20 [×2], C2×C20 [×2], C2×C20 [×2], C5×D4 [×4], C22×C10, C22×C10 [×2], C22.36C24, C4×Dic5 [×2], C4×Dic5 [×2], C10.D4 [×6], C4⋊Dic5 [×3], C23.D5 [×2], C23.D5 [×8], C5×C22⋊C4 [×2], C5×C4⋊C4, C2×Dic10, C2×Dic10 [×2], C22×Dic5 [×2], C22×C20, D4×C10, D4×C10 [×2], Dic5.14D4 [×2], C23.D10 [×2], Dic53Q8, C20⋊Q8, C20.48D4, C23.21D10, D4×Dic5, C23.18D10 [×2], C20.17D4, C20.17D4 [×2], C5×C4⋊D4, C10.362+ 1+4
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], D5, C4○D4 [×2], C24, D10 [×7], C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D5 [×7], C22.36C24, D42D5 [×2], C23×D5, C2×D42D5, D46D10, D4.10D10, C10.362+ 1+4

Smallest permutation representation of C10.362+ 1+4
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)
(1 157 23 20)(2 156 24 19)(3 155 25 18)(4 154 26 17)(5 153 27 16)(6 152 28 15)(7 151 29 14)(8 160 30 13)(9 159 21 12)(10 158 22 11)(31 134 48 142)(32 133 49 141)(33 132 50 150)(34 131 41 149)(35 140 42 148)(36 139 43 147)(37 138 44 146)(38 137 45 145)(39 136 46 144)(40 135 47 143)(51 127 68 119)(52 126 69 118)(53 125 70 117)(54 124 61 116)(55 123 62 115)(56 122 63 114)(57 121 64 113)(58 130 65 112)(59 129 66 111)(60 128 67 120)(71 99 89 107)(72 98 90 106)(73 97 81 105)(74 96 82 104)(75 95 83 103)(76 94 84 102)(77 93 85 101)(78 92 86 110)(79 91 87 109)(80 100 88 108)
(11 153)(12 154)(13 155)(14 156)(15 157)(16 158)(17 159)(18 160)(19 151)(20 152)(31 48)(32 49)(33 50)(34 41)(35 42)(36 43)(37 44)(38 45)(39 46)(40 47)(51 68)(52 69)(53 70)(54 61)(55 62)(56 63)(57 64)(58 65)(59 66)(60 67)(91 104)(92 105)(93 106)(94 107)(95 108)(96 109)(97 110)(98 101)(99 102)(100 103)(111 116)(112 117)(113 118)(114 119)(115 120)(121 126)(122 127)(123 128)(124 129)(125 130)(131 136)(132 137)(133 138)(134 139)(135 140)(141 146)(142 147)(143 148)(144 149)(145 150)
(1 137 28 150)(2 136 29 149)(3 135 30 148)(4 134 21 147)(5 133 22 146)(6 132 23 145)(7 131 24 144)(8 140 25 143)(9 139 26 142)(10 138 27 141)(11 32 153 44)(12 31 154 43)(13 40 155 42)(14 39 156 41)(15 38 157 50)(16 37 158 49)(17 36 159 48)(18 35 160 47)(19 34 151 46)(20 33 152 45)(51 94 63 107)(52 93 64 106)(53 92 65 105)(54 91 66 104)(55 100 67 103)(56 99 68 102)(57 98 69 101)(58 97 70 110)(59 96 61 109)(60 95 62 108)(71 122 84 119)(72 121 85 118)(73 130 86 117)(74 129 87 116)(75 128 88 115)(76 127 89 114)(77 126 90 113)(78 125 81 112)(79 124 82 111)(80 123 83 120)
(1 86 28 73)(2 87 29 74)(3 88 30 75)(4 89 21 76)(5 90 22 77)(6 81 23 78)(7 82 24 79)(8 83 25 80)(9 84 26 71)(10 85 27 72)(11 93 153 106)(12 94 154 107)(13 95 155 108)(14 96 156 109)(15 97 157 110)(16 98 158 101)(17 99 159 102)(18 100 160 103)(19 91 151 104)(20 92 152 105)(31 51 43 63)(32 52 44 64)(33 53 45 65)(34 54 46 66)(35 55 47 67)(36 56 48 68)(37 57 49 69)(38 58 50 70)(39 59 41 61)(40 60 42 62)(111 131 124 144)(112 132 125 145)(113 133 126 146)(114 134 127 147)(115 135 128 148)(116 136 129 149)(117 137 130 150)(118 138 121 141)(119 139 122 142)(120 140 123 143)

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

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

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

50 conjugacy classes

class 1 2A2B2C2D2E2F4A4B4C4D4E4F4G4H4I4J···4O5A5B10A···10F10G10H10I10J10K10L10M10N20A···20H20I20J20K20L
order12222224444444444···45510···10101010101010101020···2020202020
size1111444224441010101020···20222···2444488884···48888

50 irreducible representations

dim1111111111122222244444
type+++++++++++++++++---
imageC1C2C2C2C2C2C2C2C2C2C2D5C4○D4D10D10D10D102+ 1+42- 1+4D42D5D46D10D4.10D10
kernelC10.362+ 1+4Dic5.14D4C23.D10Dic53Q8C20⋊Q8C20.48D4C23.21D10D4×Dic5C23.18D10C20.17D4C5×C4⋊D4C4⋊D4C20C22⋊C4C4⋊C4C22×C4C2×D4C10C10C4C2C2
# reps1221111123124422611444

Matrix representation of C10.362+ 1+4 in GL8(𝔽41)

400000000
040000000
0035350000
006400000
000040000
000004000
000000400
000000040
,
320000000
79000000
00350000
0023380000
0000341113
000028261313
00003251117
00001625511
,
10000000
2240000000
004000000
000400000
00001000
00000100
0000130400
000017040
,
929000000
3432000000
00350000
0023380000
00003427131
000028261313
00003191711
00001619115
,
10000000
01000000
00100000
00010000
000034700
000028700
000010262014
00009212721

G:=sub<GL(8,GF(41))| [40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,35,6,0,0,0,0,0,0,35,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40],[32,7,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,3,23,0,0,0,0,0,0,5,38,0,0,0,0,0,0,0,0,34,28,3,16,0,0,0,0,1,26,25,25,0,0,0,0,1,13,11,5,0,0,0,0,13,13,17,11],[1,22,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,1,30,7,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40],[9,34,0,0,0,0,0,0,29,32,0,0,0,0,0,0,0,0,3,23,0,0,0,0,0,0,5,38,0,0,0,0,0,0,0,0,34,28,3,16,0,0,0,0,27,26,19,19,0,0,0,0,13,13,17,11,0,0,0,0,1,13,11,5],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,34,28,10,9,0,0,0,0,7,7,26,21,0,0,0,0,0,0,20,27,0,0,0,0,0,0,14,21] >;

C10.362+ 1+4 in GAP, Magma, Sage, TeX

C_{10}._{36}2_+^{1+4}
% in TeX

G:=Group("C10.36ES+(2,2)");
// GroupNames label

G:=SmallGroup(320,1275);
// by ID

G=gap.SmallGroup(320,1275);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,219,675,570,297,12550]);
// Polycyclic

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

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