G = C10.582+ 1+4 order 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⋊Q8⋊29C2, C22⋊Q8⋊23D5, C4⋊C4.101D10, (C2×Q8).79D10, D10⋊Q8⋊24C2, D10⋊3Q8⋊25C2, C22⋊C4.23D10, C4.Dic10⋊27C2, Dic5⋊Q8⋊18C2, C20.48D4⋊47C2, (C2×C10).190C24, (C2×C20).176C23, (C22×C4).252D10, C2.60(D4⋊6D10), Dic5.Q8⋊22C2, D10.12D4.3C2, D10⋊C4.8C22, C23.D10⋊26C2, 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, C5⋊1(C22.57C24), (C4×Dic5).125C22, (C2×Dic10).37C22, C10.D4.81C22, C23.23D10.3C2, C2.39(D4.10D10), C2.26(Q8.10D10), C4⋊C4⋊D5⋊25C2, (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
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, C2, C4, C22, C22, C5, C2×C4, C2×C4, D4, Q8, C23, C23, D5, C10, C10, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic5, C20, D10, C2×C10, C2×C10, C22⋊Q8, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, C4⋊Q8, Dic10, C4×D5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×Q8, C22×D5, C22×C10, C22.57C24, C4×Dic5, C10.D4, C4⋊Dic5, D10⋊C4, C23.D5, C5×C22⋊C4, C5×C4⋊C4, C2×Dic10, C2×C4×D5, C2×C5⋊D4, C22×C20, Q8×C10, C23.D10, D10.12D4, Dic5.5D4, C20⋊Q8, Dic5.Q8, C4.Dic10, D10⋊Q8, C4⋊C4⋊D5, C20.48D4, C23.23D10, Dic5⋊Q8, D10⋊3Q8, C5×C22⋊Q8, C10.582+ 1+4
Quotients: C1, C2, C22, C23, D5, C24, D10, 2+ 1+4, 2- 1+4, C22×D5, C22.57C24, C23×D5, D4⋊6D10, Q8.10D10, D4.10D10, 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 35)(2 46 21 36)(3 47 22 37)(4 48 23 38)(5 49 24 39)(6 50 25 40)(7 41 26 31)(8 42 27 32)(9 43 28 33)(10 44 29 34)(11 140 155 150)(12 131 156 141)(13 132 157 142)(14 133 158 143)(15 134 159 144)(16 135 160 145)(17 136 151 146)(18 137 152 147)(19 138 153 148)(20 139 154 149)(51 86 61 76)(52 87 62 77)(53 88 63 78)(54 89 64 79)(55 90 65 80)(56 81 66 71)(57 82 67 72)(58 83 68 73)(59 84 69 74)(60 85 70 75)(91 116 101 126)(92 117 102 127)(93 118 103 128)(94 119 104 129)(95 120 105 130)(96 111 106 121)(97 112 107 122)(98 113 108 123)(99 114 109 124)(100 115 110 125)
(1 35 6 40)(2 34 7 39)(3 33 8 38)(4 32 9 37)(5 31 10 36)(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 84 56 89)(52 83 57 88)(53 82 58 87)(54 81 59 86)(55 90 60 85)(61 74 66 79)(62 73 67 78)(63 72 68 77)(64 71 69 76)(65 80 70 75)(91 124 96 129)(92 123 97 128)(93 122 98 127)(94 121 99 126)(95 130 100 125)(101 114 106 119)(102 113 107 118)(103 112 108 117)(104 111 109 116)(105 120 110 115)(131 154 136 159)(132 153 137 158)(133 152 138 157)(134 151 139 156)(135 160 140 155)
(1 85 30 75)(2 86 21 76)(3 87 22 77)(4 88 23 78)(5 89 24 79)(6 90 25 80)(7 81 26 71)(8 82 27 72)(9 83 28 73)(10 84 29 74)(11 95 155 105)(12 96 156 106)(13 97 157 107)(14 98 158 108)(15 99 159 109)(16 100 160 110)(17 91 151 101)(18 92 152 102)(19 93 153 103)(20 94 154 104)(31 56 41 66)(32 57 42 67)(33 58 43 68)(34 59 44 69)(35 60 45 70)(36 51 46 61)(37 52 47 62)(38 53 48 63)(39 54 49 64)(40 55 50 65)(111 141 121 131)(112 142 122 132)(113 143 123 133)(114 144 124 134)(115 145 125 135)(116 146 126 136)(117 147 127 137)(118 148 128 138)(119 149 129 139)(120 150 130 140)
(1 16 30 160)(2 15 21 159)(3 14 22 158)(4 13 23 157)(5 12 24 156)(6 11 25 155)(7 20 26 154)(8 19 27 153)(9 18 28 152)(10 17 29 151)(31 144 41 134)(32 143 42 133)(33 142 43 132)(34 141 44 131)(35 150 45 140)(36 149 46 139)(37 148 47 138)(38 147 48 137)(39 146 49 136)(40 145 50 135)(51 119 61 129)(52 118 62 128)(53 117 63 127)(54 116 64 126)(55 115 65 125)(56 114 66 124)(57 113 67 123)(58 112 68 122)(59 111 69 121)(60 120 70 130)(71 94 81 104)(72 93 82 103)(73 92 83 102)(74 91 84 101)(75 100 85 110)(76 99 86 109)(77 98 87 108)(78 97 88 107)(79 96 89 106)(80 95 90 105)
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), (1,45,30,35)(2,46,21,36)(3,47,22,37)(4,48,23,38)(5,49,24,39)(6,50,25,40)(7,41,26,31)(8,42,27,32)(9,43,28,33)(10,44,29,34)(11,140,155,150)(12,131,156,141)(13,132,157,142)(14,133,158,143)(15,134,159,144)(16,135,160,145)(17,136,151,146)(18,137,152,147)(19,138,153,148)(20,139,154,149)(51,86,61,76)(52,87,62,77)(53,88,63,78)(54,89,64,79)(55,90,65,80)(56,81,66,71)(57,82,67,72)(58,83,68,73)(59,84,69,74)(60,85,70,75)(91,116,101,126)(92,117,102,127)(93,118,103,128)(94,119,104,129)(95,120,105,130)(96,111,106,121)(97,112,107,122)(98,113,108,123)(99,114,109,124)(100,115,110,125), (1,35,6,40)(2,34,7,39)(3,33,8,38)(4,32,9,37)(5,31,10,36)(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)(51,84,56,89)(52,83,57,88)(53,82,58,87)(54,81,59,86)(55,90,60,85)(61,74,66,79)(62,73,67,78)(63,72,68,77)(64,71,69,76)(65,80,70,75)(91,124,96,129)(92,123,97,128)(93,122,98,127)(94,121,99,126)(95,130,100,125)(101,114,106,119)(102,113,107,118)(103,112,108,117)(104,111,109,116)(105,120,110,115)(131,154,136,159)(132,153,137,158)(133,152,138,157)(134,151,139,156)(135,160,140,155), (1,85,30,75)(2,86,21,76)(3,87,22,77)(4,88,23,78)(5,89,24,79)(6,90,25,80)(7,81,26,71)(8,82,27,72)(9,83,28,73)(10,84,29,74)(11,95,155,105)(12,96,156,106)(13,97,157,107)(14,98,158,108)(15,99,159,109)(16,100,160,110)(17,91,151,101)(18,92,152,102)(19,93,153,103)(20,94,154,104)(31,56,41,66)(32,57,42,67)(33,58,43,68)(34,59,44,69)(35,60,45,70)(36,51,46,61)(37,52,47,62)(38,53,48,63)(39,54,49,64)(40,55,50,65)(111,141,121,131)(112,142,122,132)(113,143,123,133)(114,144,124,134)(115,145,125,135)(116,146,126,136)(117,147,127,137)(118,148,128,138)(119,149,129,139)(120,150,130,140), (1,16,30,160)(2,15,21,159)(3,14,22,158)(4,13,23,157)(5,12,24,156)(6,11,25,155)(7,20,26,154)(8,19,27,153)(9,18,28,152)(10,17,29,151)(31,144,41,134)(32,143,42,133)(33,142,43,132)(34,141,44,131)(35,150,45,140)(36,149,46,139)(37,148,47,138)(38,147,48,137)(39,146,49,136)(40,145,50,135)(51,119,61,129)(52,118,62,128)(53,117,63,127)(54,116,64,126)(55,115,65,125)(56,114,66,124)(57,113,67,123)(58,112,68,122)(59,111,69,121)(60,120,70,130)(71,94,81,104)(72,93,82,103)(73,92,83,102)(74,91,84,101)(75,100,85,110)(76,99,86,109)(77,98,87,108)(78,97,88,107)(79,96,89,106)(80,95,90,105)>;
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), (1,45,30,35)(2,46,21,36)(3,47,22,37)(4,48,23,38)(5,49,24,39)(6,50,25,40)(7,41,26,31)(8,42,27,32)(9,43,28,33)(10,44,29,34)(11,140,155,150)(12,131,156,141)(13,132,157,142)(14,133,158,143)(15,134,159,144)(16,135,160,145)(17,136,151,146)(18,137,152,147)(19,138,153,148)(20,139,154,149)(51,86,61,76)(52,87,62,77)(53,88,63,78)(54,89,64,79)(55,90,65,80)(56,81,66,71)(57,82,67,72)(58,83,68,73)(59,84,69,74)(60,85,70,75)(91,116,101,126)(92,117,102,127)(93,118,103,128)(94,119,104,129)(95,120,105,130)(96,111,106,121)(97,112,107,122)(98,113,108,123)(99,114,109,124)(100,115,110,125), (1,35,6,40)(2,34,7,39)(3,33,8,38)(4,32,9,37)(5,31,10,36)(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)(51,84,56,89)(52,83,57,88)(53,82,58,87)(54,81,59,86)(55,90,60,85)(61,74,66,79)(62,73,67,78)(63,72,68,77)(64,71,69,76)(65,80,70,75)(91,124,96,129)(92,123,97,128)(93,122,98,127)(94,121,99,126)(95,130,100,125)(101,114,106,119)(102,113,107,118)(103,112,108,117)(104,111,109,116)(105,120,110,115)(131,154,136,159)(132,153,137,158)(133,152,138,157)(134,151,139,156)(135,160,140,155), (1,85,30,75)(2,86,21,76)(3,87,22,77)(4,88,23,78)(5,89,24,79)(6,90,25,80)(7,81,26,71)(8,82,27,72)(9,83,28,73)(10,84,29,74)(11,95,155,105)(12,96,156,106)(13,97,157,107)(14,98,158,108)(15,99,159,109)(16,100,160,110)(17,91,151,101)(18,92,152,102)(19,93,153,103)(20,94,154,104)(31,56,41,66)(32,57,42,67)(33,58,43,68)(34,59,44,69)(35,60,45,70)(36,51,46,61)(37,52,47,62)(38,53,48,63)(39,54,49,64)(40,55,50,65)(111,141,121,131)(112,142,122,132)(113,143,123,133)(114,144,124,134)(115,145,125,135)(116,146,126,136)(117,147,127,137)(118,148,128,138)(119,149,129,139)(120,150,130,140), (1,16,30,160)(2,15,21,159)(3,14,22,158)(4,13,23,157)(5,12,24,156)(6,11,25,155)(7,20,26,154)(8,19,27,153)(9,18,28,152)(10,17,29,151)(31,144,41,134)(32,143,42,133)(33,142,43,132)(34,141,44,131)(35,150,45,140)(36,149,46,139)(37,148,47,138)(38,147,48,137)(39,146,49,136)(40,145,50,135)(51,119,61,129)(52,118,62,128)(53,117,63,127)(54,116,64,126)(55,115,65,125)(56,114,66,124)(57,113,67,123)(58,112,68,122)(59,111,69,121)(60,120,70,130)(71,94,81,104)(72,93,82,103)(73,92,83,102)(74,91,84,101)(75,100,85,110)(76,99,86,109)(77,98,87,108)(78,97,88,107)(79,96,89,106)(80,95,90,105) );
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)], [(1,45,30,35),(2,46,21,36),(3,47,22,37),(4,48,23,38),(5,49,24,39),(6,50,25,40),(7,41,26,31),(8,42,27,32),(9,43,28,33),(10,44,29,34),(11,140,155,150),(12,131,156,141),(13,132,157,142),(14,133,158,143),(15,134,159,144),(16,135,160,145),(17,136,151,146),(18,137,152,147),(19,138,153,148),(20,139,154,149),(51,86,61,76),(52,87,62,77),(53,88,63,78),(54,89,64,79),(55,90,65,80),(56,81,66,71),(57,82,67,72),(58,83,68,73),(59,84,69,74),(60,85,70,75),(91,116,101,126),(92,117,102,127),(93,118,103,128),(94,119,104,129),(95,120,105,130),(96,111,106,121),(97,112,107,122),(98,113,108,123),(99,114,109,124),(100,115,110,125)], [(1,35,6,40),(2,34,7,39),(3,33,8,38),(4,32,9,37),(5,31,10,36),(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),(51,84,56,89),(52,83,57,88),(53,82,58,87),(54,81,59,86),(55,90,60,85),(61,74,66,79),(62,73,67,78),(63,72,68,77),(64,71,69,76),(65,80,70,75),(91,124,96,129),(92,123,97,128),(93,122,98,127),(94,121,99,126),(95,130,100,125),(101,114,106,119),(102,113,107,118),(103,112,108,117),(104,111,109,116),(105,120,110,115),(131,154,136,159),(132,153,137,158),(133,152,138,157),(134,151,139,156),(135,160,140,155)], [(1,85,30,75),(2,86,21,76),(3,87,22,77),(4,88,23,78),(5,89,24,79),(6,90,25,80),(7,81,26,71),(8,82,27,72),(9,83,28,73),(10,84,29,74),(11,95,155,105),(12,96,156,106),(13,97,157,107),(14,98,158,108),(15,99,159,109),(16,100,160,110),(17,91,151,101),(18,92,152,102),(19,93,153,103),(20,94,154,104),(31,56,41,66),(32,57,42,67),(33,58,43,68),(34,59,44,69),(35,60,45,70),(36,51,46,61),(37,52,47,62),(38,53,48,63),(39,54,49,64),(40,55,50,65),(111,141,121,131),(112,142,122,132),(113,143,123,133),(114,144,124,134),(115,145,125,135),(116,146,126,136),(117,147,127,137),(118,148,128,138),(119,149,129,139),(120,150,130,140)], [(1,16,30,160),(2,15,21,159),(3,14,22,158),(4,13,23,157),(5,12,24,156),(6,11,25,155),(7,20,26,154),(8,19,27,153),(9,18,28,152),(10,17,29,151),(31,144,41,134),(32,143,42,133),(33,142,43,132),(34,141,44,131),(35,150,45,140),(36,149,46,139),(37,148,47,138),(38,147,48,137),(39,146,49,136),(40,145,50,135),(51,119,61,129),(52,118,62,128),(53,117,63,127),(54,116,64,126),(55,115,65,125),(56,114,66,124),(57,113,67,123),(58,112,68,122),(59,111,69,121),(60,120,70,130),(71,94,81,104),(72,93,82,103),(73,92,83,102),(74,91,84,101),(75,100,85,110),(76,99,86,109),(77,98,87,108),(78,97,88,107),(79,96,89,106),(80,95,90,105)]])
47 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4F | 4G | ··· | 4M | 5A | 5B | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 20A | ··· | 20H | 20I | ··· | 20P |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 4 | 20 | 4 | ··· | 4 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
47 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D5 | D10 | D10 | D10 | D10 | 2+ 1+4 | 2- 1+4 | D4⋊6D10 | Q8.10D10 | D4.10D10 |
| kernel | C10.582+ 1+4 | C23.D10 | D10.12D4 | Dic5.5D4 | C20⋊Q8 | Dic5.Q8 | C4.Dic10 | D10⋊Q8 | C4⋊C4⋊D5 | C20.48D4 | C23.23D10 | Dic5⋊Q8 | D10⋊3Q8 | C5×C22⋊Q8 | C22⋊Q8 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C10 | C10 | C2 | C2 | C2 |
| # reps | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 4 | 6 | 2 | 2 | 1 | 2 | 4 | 4 | 4 |
Matrix representation of C10.582+ 1+4 ►in GL10(𝔽41)
| 7 | 7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 34 | 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 | 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 | 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 |
| 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7 | 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 | 1 | 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 |
| 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 | 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 | 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 |
| 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7 | 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 |
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