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G = C10.582+ 1+4order 320 = 26·5

58th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.582+ 1+4, C10.252- 1+4, C20⋊Q829C2, C22⋊Q823D5, C4⋊C4.101D10, (C2×Q8).79D10, D10⋊Q824C2, D103Q825C2, C22⋊C4.23D10, C4.Dic1027C2, Dic5⋊Q818C2, C20.48D447C2, (C2×C10).190C24, (C2×C20).176C23, (C22×C4).252D10, C2.60(D46D10), Dic5.Q822C2, D10.12D4.3C2, D10⋊C4.8C22, C23.D1026C2, C4⋊Dic5.222C22, Dic5.5D4.3C2, (Q8×C10).119C22, (C2×Dic5).96C23, (C22×D5).81C23, C23.126(C22×D5), C22.211(C23×D5), C23.D5.36C22, (C22×C20).318C22, (C22×C10).218C23, C51(C22.57C24), (C4×Dic5).125C22, (C2×Dic10).37C22, C10.D4.81C22, C23.23D10.3C2, C2.39(D4.10D10), C2.26(Q8.10D10), C4⋊C4⋊D525C2, (C5×C22⋊Q8)⋊26C2, (C2×C4×D5).115C22, (C5×C4⋊C4).170C22, (C2×C4).187(C22×D5), (C2×C5⋊D4).42C22, (C5×C22⋊C4).45C22, SmallGroup(320,1318)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C10.582+ 1+4
C1C5C10C2×C10C22×D5C2×C4×D5D10.12D4 — C10.582+ 1+4
C5C2×C10 — C10.582+ 1+4
C1C22C22⋊Q8

Generators and relations for C10.582+ 1+4
 G = < a,b,c,d,e | a10=b4=1, c2=a5, d2=e2=b2, ab=ba, cac-1=eae-1=a-1, ad=da, cbc-1=a5b-1, bd=db, ebe-1=a5b, dcd-1=a5c, ce=ec, ede-1=b2d >

Subgroups: 646 in 196 conjugacy classes, 91 normal (all characteristic)
C1, C2 [×3], C2 [×2], C4 [×13], C22, C22 [×6], C5, C2×C4 [×6], C2×C4 [×9], D4, Q8 [×3], C23, C23, D5, C10 [×3], C10, C42 [×3], C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4 [×3], C4⋊C4 [×13], C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8 [×2], Dic5 [×7], C20 [×6], D10 [×3], C2×C10, C2×C10 [×3], C22⋊Q8, C22⋊Q8 [×3], C22.D4 [×2], C4.4D4, C42.C2 [×2], C422C2 [×4], C4⋊Q8 [×2], Dic10 [×2], C4×D5, C2×Dic5 [×7], C5⋊D4, C2×C20 [×6], C2×C20, C5×Q8, C22×D5, C22×C10, C22.57C24, C4×Dic5 [×3], C10.D4 [×9], C4⋊Dic5 [×4], D10⋊C4 [×5], C23.D5 [×3], C5×C22⋊C4 [×2], C5×C4⋊C4 [×3], C2×Dic10 [×2], C2×C4×D5, C2×C5⋊D4, C22×C20, Q8×C10, C23.D10 [×2], D10.12D4, Dic5.5D4, C20⋊Q8, Dic5.Q8, C4.Dic10, D10⋊Q8, C4⋊C4⋊D5 [×2], C20.48D4, C23.23D10, Dic5⋊Q8, D103Q8, C5×C22⋊Q8, C10.582+ 1+4
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], D5, C24, D10 [×7], 2+ 1+4, 2- 1+4 [×2], C22×D5 [×7], C22.57C24, C23×D5, D46D10, Q8.10D10, D4.10D10, C10.582+ 1+4

Smallest permutation representation of C10.582+ 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 45 30 37)(2 46 21 38)(3 47 22 39)(4 48 23 40)(5 49 24 31)(6 50 25 32)(7 41 26 33)(8 42 27 34)(9 43 28 35)(10 44 29 36)(11 132 157 150)(12 133 158 141)(13 134 159 142)(14 135 160 143)(15 136 151 144)(16 137 152 145)(17 138 153 146)(18 139 154 147)(19 140 155 148)(20 131 156 149)(51 84 69 76)(52 85 70 77)(53 86 61 78)(54 87 62 79)(55 88 63 80)(56 89 64 71)(57 90 65 72)(58 81 66 73)(59 82 67 74)(60 83 68 75)(91 116 109 124)(92 117 110 125)(93 118 101 126)(94 119 102 127)(95 120 103 128)(96 111 104 129)(97 112 105 130)(98 113 106 121)(99 114 107 122)(100 115 108 123)
(1 37 6 32)(2 36 7 31)(3 35 8 40)(4 34 9 39)(5 33 10 38)(11 145 16 150)(12 144 17 149)(13 143 18 148)(14 142 19 147)(15 141 20 146)(21 44 26 49)(22 43 27 48)(23 42 28 47)(24 41 29 46)(25 50 30 45)(51 86 56 81)(52 85 57 90)(53 84 58 89)(54 83 59 88)(55 82 60 87)(61 76 66 71)(62 75 67 80)(63 74 68 79)(64 73 69 78)(65 72 70 77)(91 126 96 121)(92 125 97 130)(93 124 98 129)(94 123 99 128)(95 122 100 127)(101 116 106 111)(102 115 107 120)(103 114 108 119)(104 113 109 118)(105 112 110 117)(131 158 136 153)(132 157 137 152)(133 156 138 151)(134 155 139 160)(135 154 140 159)
(1 85 30 77)(2 86 21 78)(3 87 22 79)(4 88 23 80)(5 89 24 71)(6 90 25 72)(7 81 26 73)(8 82 27 74)(9 83 28 75)(10 84 29 76)(11 97 157 105)(12 98 158 106)(13 99 159 107)(14 100 160 108)(15 91 151 109)(16 92 152 110)(17 93 153 101)(18 94 154 102)(19 95 155 103)(20 96 156 104)(31 56 49 64)(32 57 50 65)(33 58 41 66)(34 59 42 67)(35 60 43 68)(36 51 44 69)(37 52 45 70)(38 53 46 61)(39 54 47 62)(40 55 48 63)(111 149 129 131)(112 150 130 132)(113 141 121 133)(114 142 122 134)(115 143 123 135)(116 144 124 136)(117 145 125 137)(118 146 126 138)(119 147 127 139)(120 148 128 140)
(1 16 30 152)(2 15 21 151)(3 14 22 160)(4 13 23 159)(5 12 24 158)(6 11 25 157)(7 20 26 156)(8 19 27 155)(9 18 28 154)(10 17 29 153)(31 146 49 138)(32 145 50 137)(33 144 41 136)(34 143 42 135)(35 142 43 134)(36 141 44 133)(37 150 45 132)(38 149 46 131)(39 148 47 140)(40 147 48 139)(51 113 69 121)(52 112 70 130)(53 111 61 129)(54 120 62 128)(55 119 63 127)(56 118 64 126)(57 117 65 125)(58 116 66 124)(59 115 67 123)(60 114 68 122)(71 98 89 106)(72 97 90 105)(73 96 81 104)(74 95 82 103)(75 94 83 102)(76 93 84 101)(77 92 85 110)(78 91 86 109)(79 100 87 108)(80 99 88 107)

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

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

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

47 conjugacy classes

class 1 2A2B2C2D2E4A···4F4G···4M5A5B10A···10F10G10H10I10J20A···20H20I···20P
order1222224···44···45510···101010101020···2020···20
size11114204···420···20222···244444···48···8

47 irreducible representations

dim111111111111112222244444
type++++++++++++++++++++--
imageC1C2C2C2C2C2C2C2C2C2C2C2C2C2D5D10D10D10D102+ 1+42- 1+4D46D10Q8.10D10D4.10D10
kernelC10.582+ 1+4C23.D10D10.12D4Dic5.5D4C20⋊Q8Dic5.Q8C4.Dic10D10⋊Q8C4⋊C4⋊D5C20.48D4C23.23D10Dic5⋊Q8D103Q8C5×C22⋊Q8C22⋊Q8C22⋊C4C4⋊C4C22×C4C2×Q8C10C10C2C2C2
# reps121111112111112462212444

Matrix representation of C10.582+ 1+4 in GL10(𝔽41)

7700000000
344000000000
0010000000
0001000000
0000100000
0000010000
00000040000
00000004000
00000000400
00000000040
,
40000000000
04000000000
0001000000
00400000000
0000010000
00004000000
00000004000
0000001000
00000000040
0000000010
,
40000000000
7100000000
0001000000
0010000000
00000400000
00004000000
0000000100
00000040000
00000000040
0000000010
,
40000000000
04000000000
0000010000
00004000000
0001000000
00400000000
00000000040
0000000010
00000004000
0000001000
,
40000000000
7100000000
00210030000
000213800000
000382000000
00300200000
000000002734
000000003414
000000273400
000000341400

G:=sub<GL(10,GF(41))| [7,34,0,0,0,0,0,0,0,0,7,40,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0],[40,7,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0],[40,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0],[40,7,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,21,0,0,3,0,0,0,0,0,0,0,21,38,0,0,0,0,0,0,0,0,38,20,0,0,0,0,0,0,0,3,0,0,20,0,0,0,0,0,0,0,0,0,0,0,0,27,34,0,0,0,0,0,0,0,0,34,14,0,0,0,0,0,0,27,34,0,0,0,0,0,0,0,0,34,14,0,0] >;

C10.582+ 1+4 in GAP, Magma, Sage, TeX

C_{10}._{58}2_+^{1+4}
% in TeX

G:=Group("C10.58ES+(2,2)");
// GroupNames label

G:=SmallGroup(320,1318);
// by ID

G=gap.SmallGroup(320,1318);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,758,219,1571,570,136,12550]);
// Polycyclic

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

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