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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

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C10 — C10.582+ 1+4
 Chief series C1 — C5 — C10 — C2×C10 — C22×D5 — C2×C4×D5 — D10.12D4 — C10.582+ 1+4
 Lower central C5 — C2×C10 — C10.582+ 1+4
 Upper central C1 — C22 — C22⋊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, 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, C422C2, 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, D103Q8, 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, 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 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`

׿
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