G = C10.442- 1+4 order 320 = 26·5
44th non-split extension by C10 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.442- 1+4, (C22×Q8)⋊8D5, (C2×C20).216D4, C20.261(C2×D4), D10⋊3Q8⋊41C2, (C2×Q8).188D10, Dic5⋊Q8⋊30C2, C20.23D4⋊29C2, (C2×C10).308C24, (C2×C20).648C23, (C22×C4).278D10, C10.156(C22×D4), (C2×D20).287C22, C4⋊Dic5.390C22, (Q8×C10).235C22, C23.239(C22×D5), C22.319(C23×D5), D10⋊C4.77C22, C23.23D10⋊29C2, C23.21D10⋊34C2, (C22×C20).440C22, (C22×C10).426C23, C5⋊6(C23.38C23), (C4×Dic5).179C22, (C2×Dic5).159C23, C10.D4.90C22, (C22×D5).134C23, C23.D5.132C22, C2.44(Q8.10D10), (C2×Dic10).316C22, (Q8×C2×C10)⋊7C2, C4.99(C2×C5⋊D4), (C2×C4○D20).25C2, (C2×C10).590(C2×D4), (C2×C4).94(C5⋊D4), (C2×C4×D5).174C22, C2.29(C22×C5⋊D4), C22.37(C2×C5⋊D4), (C2×C4).634(C22×D5), (C2×C5⋊D4).146C22, SmallGroup(320,1488)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.442- 1+4
G = < a,b,c,d,e | a10=b4=1, c2=a5, d2=e2=a5b2, bab-1=cac-1=a-1, ad=da, ae=ea, cbc-1=a5b-1, dbd-1=ebe-1=a5b, dcd-1=ece-1=a5c, ede-1=a5b2d >
Subgroups: 846 in 270 conjugacy classes, 111 normal (21 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C5, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D5, C10, C10, C10, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic5, C20, C20, D10, C2×C10, C2×C10, C2×C10, C42⋊C2, C22⋊Q8, C22.D4, C4.4D4, C4⋊Q8, C22×Q8, C2×C4○D4, Dic10, C4×D5, D20, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C2×C20, C5×Q8, C22×D5, C22×C10, C23.38C23, C4×Dic5, C10.D4, C4⋊Dic5, D10⋊C4, C23.D5, C2×Dic10, C2×C4×D5, C2×D20, C4○D20, C2×C5⋊D4, C22×C20, C22×C20, Q8×C10, Q8×C10, C23.21D10, C23.23D10, Dic5⋊Q8, D10⋊3Q8, C20.23D4, C2×C4○D20, Q8×C2×C10, C10.442- 1+4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C24, D10, C22×D4, 2- 1+4, C5⋊D4, C22×D5, C23.38C23, C2×C5⋊D4, C23×D5, Q8.10D10, C22×C5⋊D4, C10.442- 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 33 25 50)(2 32 26 49)(3 31 27 48)(4 40 28 47)(5 39 29 46)(6 38 30 45)(7 37 21 44)(8 36 22 43)(9 35 23 42)(10 34 24 41)(11 133 158 150)(12 132 159 149)(13 131 160 148)(14 140 151 147)(15 139 152 146)(16 138 153 145)(17 137 154 144)(18 136 155 143)(19 135 156 142)(20 134 157 141)(51 82 68 75)(52 81 69 74)(53 90 70 73)(54 89 61 72)(55 88 62 71)(56 87 63 80)(57 86 64 79)(58 85 65 78)(59 84 66 77)(60 83 67 76)(91 122 108 115)(92 121 109 114)(93 130 110 113)(94 129 101 112)(95 128 102 111)(96 127 103 120)(97 126 104 119)(98 125 105 118)(99 124 106 117)(100 123 107 116)
(1 73 6 78)(2 72 7 77)(3 71 8 76)(4 80 9 75)(5 79 10 74)(11 93 16 98)(12 92 17 97)(13 91 18 96)(14 100 19 95)(15 99 20 94)(21 84 26 89)(22 83 27 88)(23 82 28 87)(24 81 29 86)(25 90 30 85)(31 67 36 62)(32 66 37 61)(33 65 38 70)(34 64 39 69)(35 63 40 68)(41 57 46 52)(42 56 47 51)(43 55 48 60)(44 54 49 59)(45 53 50 58)(101 152 106 157)(102 151 107 156)(103 160 108 155)(104 159 109 154)(105 158 110 153)(111 135 116 140)(112 134 117 139)(113 133 118 138)(114 132 119 137)(115 131 120 136)(121 149 126 144)(122 148 127 143)(123 147 128 142)(124 146 129 141)(125 145 130 150)
(1 153 30 11)(2 154 21 12)(3 155 22 13)(4 156 23 14)(5 157 24 15)(6 158 25 16)(7 159 26 17)(8 160 27 18)(9 151 28 19)(10 152 29 20)(31 148 43 136)(32 149 44 137)(33 150 45 138)(34 141 46 139)(35 142 47 140)(36 143 48 131)(37 144 49 132)(38 145 50 133)(39 146 41 134)(40 147 42 135)(51 116 63 128)(52 117 64 129)(53 118 65 130)(54 119 66 121)(55 120 67 122)(56 111 68 123)(57 112 69 124)(58 113 70 125)(59 114 61 126)(60 115 62 127)(71 108 83 96)(72 109 84 97)(73 110 85 98)(74 101 86 99)(75 102 87 100)(76 103 88 91)(77 104 89 92)(78 105 90 93)(79 106 81 94)(80 107 82 95)
(1 45 30 33)(2 46 21 34)(3 47 22 35)(4 48 23 36)(5 49 24 37)(6 50 25 38)(7 41 26 39)(8 42 27 40)(9 43 28 31)(10 44 29 32)(11 138 153 150)(12 139 154 141)(13 140 155 142)(14 131 156 143)(15 132 157 144)(16 133 158 145)(17 134 159 146)(18 135 160 147)(19 136 151 148)(20 137 152 149)(51 88 63 76)(52 89 64 77)(53 90 65 78)(54 81 66 79)(55 82 67 80)(56 83 68 71)(57 84 69 72)(58 85 70 73)(59 86 61 74)(60 87 62 75)(91 116 103 128)(92 117 104 129)(93 118 105 130)(94 119 106 121)(95 120 107 122)(96 111 108 123)(97 112 109 124)(98 113 110 125)(99 114 101 126)(100 115 102 127)
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), (1,33,25,50)(2,32,26,49)(3,31,27,48)(4,40,28,47)(5,39,29,46)(6,38,30,45)(7,37,21,44)(8,36,22,43)(9,35,23,42)(10,34,24,41)(11,133,158,150)(12,132,159,149)(13,131,160,148)(14,140,151,147)(15,139,152,146)(16,138,153,145)(17,137,154,144)(18,136,155,143)(19,135,156,142)(20,134,157,141)(51,82,68,75)(52,81,69,74)(53,90,70,73)(54,89,61,72)(55,88,62,71)(56,87,63,80)(57,86,64,79)(58,85,65,78)(59,84,66,77)(60,83,67,76)(91,122,108,115)(92,121,109,114)(93,130,110,113)(94,129,101,112)(95,128,102,111)(96,127,103,120)(97,126,104,119)(98,125,105,118)(99,124,106,117)(100,123,107,116), (1,73,6,78)(2,72,7,77)(3,71,8,76)(4,80,9,75)(5,79,10,74)(11,93,16,98)(12,92,17,97)(13,91,18,96)(14,100,19,95)(15,99,20,94)(21,84,26,89)(22,83,27,88)(23,82,28,87)(24,81,29,86)(25,90,30,85)(31,67,36,62)(32,66,37,61)(33,65,38,70)(34,64,39,69)(35,63,40,68)(41,57,46,52)(42,56,47,51)(43,55,48,60)(44,54,49,59)(45,53,50,58)(101,152,106,157)(102,151,107,156)(103,160,108,155)(104,159,109,154)(105,158,110,153)(111,135,116,140)(112,134,117,139)(113,133,118,138)(114,132,119,137)(115,131,120,136)(121,149,126,144)(122,148,127,143)(123,147,128,142)(124,146,129,141)(125,145,130,150), (1,153,30,11)(2,154,21,12)(3,155,22,13)(4,156,23,14)(5,157,24,15)(6,158,25,16)(7,159,26,17)(8,160,27,18)(9,151,28,19)(10,152,29,20)(31,148,43,136)(32,149,44,137)(33,150,45,138)(34,141,46,139)(35,142,47,140)(36,143,48,131)(37,144,49,132)(38,145,50,133)(39,146,41,134)(40,147,42,135)(51,116,63,128)(52,117,64,129)(53,118,65,130)(54,119,66,121)(55,120,67,122)(56,111,68,123)(57,112,69,124)(58,113,70,125)(59,114,61,126)(60,115,62,127)(71,108,83,96)(72,109,84,97)(73,110,85,98)(74,101,86,99)(75,102,87,100)(76,103,88,91)(77,104,89,92)(78,105,90,93)(79,106,81,94)(80,107,82,95), (1,45,30,33)(2,46,21,34)(3,47,22,35)(4,48,23,36)(5,49,24,37)(6,50,25,38)(7,41,26,39)(8,42,27,40)(9,43,28,31)(10,44,29,32)(11,138,153,150)(12,139,154,141)(13,140,155,142)(14,131,156,143)(15,132,157,144)(16,133,158,145)(17,134,159,146)(18,135,160,147)(19,136,151,148)(20,137,152,149)(51,88,63,76)(52,89,64,77)(53,90,65,78)(54,81,66,79)(55,82,67,80)(56,83,68,71)(57,84,69,72)(58,85,70,73)(59,86,61,74)(60,87,62,75)(91,116,103,128)(92,117,104,129)(93,118,105,130)(94,119,106,121)(95,120,107,122)(96,111,108,123)(97,112,109,124)(98,113,110,125)(99,114,101,126)(100,115,102,127)>;
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), (1,33,25,50)(2,32,26,49)(3,31,27,48)(4,40,28,47)(5,39,29,46)(6,38,30,45)(7,37,21,44)(8,36,22,43)(9,35,23,42)(10,34,24,41)(11,133,158,150)(12,132,159,149)(13,131,160,148)(14,140,151,147)(15,139,152,146)(16,138,153,145)(17,137,154,144)(18,136,155,143)(19,135,156,142)(20,134,157,141)(51,82,68,75)(52,81,69,74)(53,90,70,73)(54,89,61,72)(55,88,62,71)(56,87,63,80)(57,86,64,79)(58,85,65,78)(59,84,66,77)(60,83,67,76)(91,122,108,115)(92,121,109,114)(93,130,110,113)(94,129,101,112)(95,128,102,111)(96,127,103,120)(97,126,104,119)(98,125,105,118)(99,124,106,117)(100,123,107,116), (1,73,6,78)(2,72,7,77)(3,71,8,76)(4,80,9,75)(5,79,10,74)(11,93,16,98)(12,92,17,97)(13,91,18,96)(14,100,19,95)(15,99,20,94)(21,84,26,89)(22,83,27,88)(23,82,28,87)(24,81,29,86)(25,90,30,85)(31,67,36,62)(32,66,37,61)(33,65,38,70)(34,64,39,69)(35,63,40,68)(41,57,46,52)(42,56,47,51)(43,55,48,60)(44,54,49,59)(45,53,50,58)(101,152,106,157)(102,151,107,156)(103,160,108,155)(104,159,109,154)(105,158,110,153)(111,135,116,140)(112,134,117,139)(113,133,118,138)(114,132,119,137)(115,131,120,136)(121,149,126,144)(122,148,127,143)(123,147,128,142)(124,146,129,141)(125,145,130,150), (1,153,30,11)(2,154,21,12)(3,155,22,13)(4,156,23,14)(5,157,24,15)(6,158,25,16)(7,159,26,17)(8,160,27,18)(9,151,28,19)(10,152,29,20)(31,148,43,136)(32,149,44,137)(33,150,45,138)(34,141,46,139)(35,142,47,140)(36,143,48,131)(37,144,49,132)(38,145,50,133)(39,146,41,134)(40,147,42,135)(51,116,63,128)(52,117,64,129)(53,118,65,130)(54,119,66,121)(55,120,67,122)(56,111,68,123)(57,112,69,124)(58,113,70,125)(59,114,61,126)(60,115,62,127)(71,108,83,96)(72,109,84,97)(73,110,85,98)(74,101,86,99)(75,102,87,100)(76,103,88,91)(77,104,89,92)(78,105,90,93)(79,106,81,94)(80,107,82,95), (1,45,30,33)(2,46,21,34)(3,47,22,35)(4,48,23,36)(5,49,24,37)(6,50,25,38)(7,41,26,39)(8,42,27,40)(9,43,28,31)(10,44,29,32)(11,138,153,150)(12,139,154,141)(13,140,155,142)(14,131,156,143)(15,132,157,144)(16,133,158,145)(17,134,159,146)(18,135,160,147)(19,136,151,148)(20,137,152,149)(51,88,63,76)(52,89,64,77)(53,90,65,78)(54,81,66,79)(55,82,67,80)(56,83,68,71)(57,84,69,72)(58,85,70,73)(59,86,61,74)(60,87,62,75)(91,116,103,128)(92,117,104,129)(93,118,105,130)(94,119,106,121)(95,120,107,122)(96,111,108,123)(97,112,109,124)(98,113,110,125)(99,114,101,126)(100,115,102,127) );
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)], [(1,33,25,50),(2,32,26,49),(3,31,27,48),(4,40,28,47),(5,39,29,46),(6,38,30,45),(7,37,21,44),(8,36,22,43),(9,35,23,42),(10,34,24,41),(11,133,158,150),(12,132,159,149),(13,131,160,148),(14,140,151,147),(15,139,152,146),(16,138,153,145),(17,137,154,144),(18,136,155,143),(19,135,156,142),(20,134,157,141),(51,82,68,75),(52,81,69,74),(53,90,70,73),(54,89,61,72),(55,88,62,71),(56,87,63,80),(57,86,64,79),(58,85,65,78),(59,84,66,77),(60,83,67,76),(91,122,108,115),(92,121,109,114),(93,130,110,113),(94,129,101,112),(95,128,102,111),(96,127,103,120),(97,126,104,119),(98,125,105,118),(99,124,106,117),(100,123,107,116)], [(1,73,6,78),(2,72,7,77),(3,71,8,76),(4,80,9,75),(5,79,10,74),(11,93,16,98),(12,92,17,97),(13,91,18,96),(14,100,19,95),(15,99,20,94),(21,84,26,89),(22,83,27,88),(23,82,28,87),(24,81,29,86),(25,90,30,85),(31,67,36,62),(32,66,37,61),(33,65,38,70),(34,64,39,69),(35,63,40,68),(41,57,46,52),(42,56,47,51),(43,55,48,60),(44,54,49,59),(45,53,50,58),(101,152,106,157),(102,151,107,156),(103,160,108,155),(104,159,109,154),(105,158,110,153),(111,135,116,140),(112,134,117,139),(113,133,118,138),(114,132,119,137),(115,131,120,136),(121,149,126,144),(122,148,127,143),(123,147,128,142),(124,146,129,141),(125,145,130,150)], [(1,153,30,11),(2,154,21,12),(3,155,22,13),(4,156,23,14),(5,157,24,15),(6,158,25,16),(7,159,26,17),(8,160,27,18),(9,151,28,19),(10,152,29,20),(31,148,43,136),(32,149,44,137),(33,150,45,138),(34,141,46,139),(35,142,47,140),(36,143,48,131),(37,144,49,132),(38,145,50,133),(39,146,41,134),(40,147,42,135),(51,116,63,128),(52,117,64,129),(53,118,65,130),(54,119,66,121),(55,120,67,122),(56,111,68,123),(57,112,69,124),(58,113,70,125),(59,114,61,126),(60,115,62,127),(71,108,83,96),(72,109,84,97),(73,110,85,98),(74,101,86,99),(75,102,87,100),(76,103,88,91),(77,104,89,92),(78,105,90,93),(79,106,81,94),(80,107,82,95)], [(1,45,30,33),(2,46,21,34),(3,47,22,35),(4,48,23,36),(5,49,24,37),(6,50,25,38),(7,41,26,39),(8,42,27,40),(9,43,28,31),(10,44,29,32),(11,138,153,150),(12,139,154,141),(13,140,155,142),(14,131,156,143),(15,132,157,144),(16,133,158,145),(17,134,159,146),(18,135,160,147),(19,136,151,148),(20,137,152,149),(51,88,63,76),(52,89,64,77),(53,90,65,78),(54,81,66,79),(55,82,67,80),(56,83,68,71),(57,84,69,72),(58,85,70,73),(59,86,61,74),(60,87,62,75),(91,116,103,128),(92,117,104,129),(93,118,105,130),(94,119,106,121),(95,120,107,122),(96,111,108,123),(97,112,109,124),(98,113,110,125),(99,114,101,126),(100,115,102,127)]])
62 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4N | 5A | 5B | 10A | ··· | 10N | 20A | ··· | 20X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 20 | 20 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
62 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D5 | D10 | D10 | C5⋊D4 | 2- 1+4 | Q8.10D10 |
| kernel | C10.442- 1+4 | C23.21D10 | C23.23D10 | Dic5⋊Q8 | D10⋊3Q8 | C20.23D4 | C2×C4○D20 | Q8×C2×C10 | C2×C20 | C22×Q8 | C22×C4 | C2×Q8 | C2×C4 | C10 | C2 |
| # reps | 1 | 1 | 4 | 2 | 4 | 2 | 1 | 1 | 4 | 2 | 6 | 8 | 16 | 2 | 8 |
Matrix representation of C10.442- 1+4 ►in GL6(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 35 | 0 | 0 |
| 0 | 0 | 7 | 35 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 35 |
| 0 | 0 | 0 | 0 | 7 | 35 |
| 40 | 40 | 0 | 0 | 0 | 0 |
| 2 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 35 | 5 | 0 | 0 |
| 0 | 0 | 34 | 6 | 0 | 0 |
| 0 | 0 | 12 | 31 | 6 | 36 |
| 0 | 0 | 14 | 29 | 7 | 35 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 39 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 38 | 0 | 0 |
| 0 | 0 | 38 | 20 | 0 | 0 |
| 0 | 0 | 40 | 6 | 20 | 3 |
| 0 | 0 | 6 | 1 | 3 | 21 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 27 | 40 | 0 |
| 0 | 0 | 30 | 33 | 0 | 40 |
| 0 | 0 | 27 | 28 | 35 | 14 |
| 0 | 0 | 22 | 14 | 11 | 8 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 | 0 | 1 |
| 0 | 0 | 39 | 0 | 40 | 0 |
| 0 | 0 | 0 | 39 | 0 | 40 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,0,7,0,0,0,0,35,35,0,0,0,0,0,0,0,7,0,0,0,0,35,35],[40,2,0,0,0,0,40,1,0,0,0,0,0,0,35,34,12,14,0,0,5,6,31,29,0,0,0,0,6,7,0,0,0,0,36,35],[1,39,0,0,0,0,1,40,0,0,0,0,0,0,21,38,40,6,0,0,38,20,6,1,0,0,0,0,20,3,0,0,0,0,3,21],[1,0,0,0,0,0,1,40,0,0,0,0,0,0,6,30,27,22,0,0,27,33,28,14,0,0,40,0,35,11,0,0,0,40,14,8],[1,0,0,0,0,0,1,40,0,0,0,0,0,0,1,0,39,0,0,0,0,1,0,39,0,0,1,0,40,0,0,0,0,1,0,40] >;
C10.442- 1+4 in GAP, Magma, Sage, TeX
C_{10}._{44}2_-^{1+4} % in TeX
G:=Group("C10.44ES-(2,2)"); // GroupNames label
G:=SmallGroup(320,1488);
// by ID
G=gap.SmallGroup(320,1488);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,758,675,570,136,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=1,c^2=a^5,d^2=e^2=a^5*b^2,b*a*b^-1=c*a*c^-1=a^-1,a*d=d*a,a*e=e*a,c*b*c^-1=a^5*b^-1,d*b*d^-1=e*b*e^-1=a^5*b,d*c*d^-1=e*c*e^-1=a^5*c,e*d*e^-1=a^5*b^2*d>;
// generators/relations