G = C10.1182+ 1+4 order 320 = 26·5
27th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.1182+ 1+4, C5⋊D4⋊2Q8, C20⋊Q8⋊26C2, C5⋊5(D4⋊3Q8), C22⋊Q8⋊12D5, C4⋊C4.192D10, (Q8×Dic5)⋊13C2, C22.1(Q8×D5), D10.21(C2×Q8), D10⋊2Q8⋊28C2, D10⋊3Q8⋊17C2, (C2×C20).58C23, (C2×Q8).129D10, C22⋊C4.60D10, Dic5.23(C2×Q8), C20.210(C4○D4), C4.99(D4⋊2D5), C10.37(C22×Q8), (C2×C10).179C24, Dic5⋊4D4.2C2, (C22×C4).241D10, C2.36(D4⋊8D10), Dic5.Q8⋊18C2, C4⋊Dic5.374C22, (Q8×C10).110C22, (C2×Dic5).90C23, C22.200(C23×D5), C23.192(C22×D5), Dic5.14D4⋊25C2, D10⋊C4.24C22, (C22×C20).258C22, (C22×C10).207C23, (C4×Dic5).116C22, (C22×D5).211C23, C23.D5.119C22, (C2×Dic10).166C22, C10.D4.118C22, (C22×Dic5).120C22, (D5×C4⋊C4)⋊27C2, C2.20(C2×Q8×D5), (C4×C5⋊D4).8C2, (C2×C10).8(C2×Q8), (C2×C4⋊Dic5)⋊42C2, C10.90(C2×C4○D4), (C5×C22⋊Q8)⋊15C2, C2.46(C2×D4⋊2D5), (C2×C4×D5).108C22, (C5×C4⋊C4).161C22, (C2×C4).184(C22×D5), (C2×C5⋊D4).134C22, (C5×C22⋊C4).34C22, SmallGroup(320,1307)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.1182+ 1+4
G = < a,b,c,d,e | a10=b4=c2=1, d2=b2, e2=a5, ab=ba, cac=a-1, ad=da, ae=ea, cbc=a5b-1, bd=db, ebe-1=a5b, cd=dc, ce=ec, ede-1=b2d >
Subgroups: 742 in 228 conjugacy classes, 107 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C5, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D5, C10, C10, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic5, Dic5, C20, C20, D10, D10, C2×C10, C2×C10, C2×C10, C2×C4⋊C4, C4×D4, C4×Q8, C22⋊Q8, C22⋊Q8, C42.C2, C4⋊Q8, Dic10, C4×D5, C2×Dic5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C2×C20, C5×Q8, C22×D5, C22×C10, D4⋊3Q8, C4×Dic5, C4×Dic5, C10.D4, C10.D4, C4⋊Dic5, C4⋊Dic5, D10⋊C4, D10⋊C4, C23.D5, C5×C22⋊C4, C5×C4⋊C4, C5×C4⋊C4, C2×Dic10, C2×C4×D5, C2×C4×D5, C22×Dic5, C2×C5⋊D4, C22×C20, Q8×C10, Dic5.14D4, Dic5⋊4D4, C20⋊Q8, Dic5.Q8, D5×C4⋊C4, D10⋊2Q8, C2×C4⋊Dic5, C4×C5⋊D4, Q8×Dic5, D10⋊3Q8, C5×C22⋊Q8, C10.1182+ 1+4
Quotients: C1, C2, C22, Q8, C23, D5, C2×Q8, C4○D4, C24, D10, C22×Q8, C2×C4○D4, 2+ 1+4, C22×D5, D4⋊3Q8, D4⋊2D5, Q8×D5, C23×D5, C2×D4⋊2D5, C2×Q8×D5, D4⋊8D10, C10.1182+ 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)
(1 145 24 133)(2 146 25 134)(3 147 26 135)(4 148 27 136)(5 149 28 137)(6 150 29 138)(7 141 30 139)(8 142 21 140)(9 143 22 131)(10 144 23 132)(11 33 153 45)(12 34 154 46)(13 35 155 47)(14 36 156 48)(15 37 157 49)(16 38 158 50)(17 39 159 41)(18 40 160 42)(19 31 151 43)(20 32 152 44)(51 103 63 91)(52 104 64 92)(53 105 65 93)(54 106 66 94)(55 107 67 95)(56 108 68 96)(57 109 69 97)(58 110 70 98)(59 101 61 99)(60 102 62 100)(71 123 83 111)(72 124 84 112)(73 125 85 113)(74 126 86 114)(75 127 87 115)(76 128 88 116)(77 129 89 117)(78 130 90 118)(79 121 81 119)(80 122 82 120)
(2 10)(3 9)(4 8)(5 7)(11 158)(12 157)(13 156)(14 155)(15 154)(16 153)(17 152)(18 151)(19 160)(20 159)(21 27)(22 26)(23 25)(28 30)(31 35)(32 34)(36 40)(37 39)(41 49)(42 48)(43 47)(44 46)(51 55)(52 54)(56 60)(57 59)(61 69)(62 68)(63 67)(64 66)(71 75)(72 74)(76 80)(77 79)(81 89)(82 88)(83 87)(84 86)(91 102)(92 101)(93 110)(94 109)(95 108)(96 107)(97 106)(98 105)(99 104)(100 103)(111 122)(112 121)(113 130)(114 129)(115 128)(116 127)(117 126)(118 125)(119 124)(120 123)(131 142)(132 141)(133 150)(134 149)(135 148)(136 147)(137 146)(138 145)(139 144)(140 143)
(1 65 24 53)(2 66 25 54)(3 67 26 55)(4 68 27 56)(5 69 28 57)(6 70 29 58)(7 61 30 59)(8 62 21 60)(9 63 22 51)(10 64 23 52)(11 113 153 125)(12 114 154 126)(13 115 155 127)(14 116 156 128)(15 117 157 129)(16 118 158 130)(17 119 159 121)(18 120 160 122)(19 111 151 123)(20 112 152 124)(31 71 43 83)(32 72 44 84)(33 73 45 85)(34 74 46 86)(35 75 47 87)(36 76 48 88)(37 77 49 89)(38 78 50 90)(39 79 41 81)(40 80 42 82)(91 131 103 143)(92 132 104 144)(93 133 105 145)(94 134 106 146)(95 135 107 147)(96 136 108 148)(97 137 109 149)(98 138 110 150)(99 139 101 141)(100 140 102 142)
(1 78 6 73)(2 79 7 74)(3 80 8 75)(4 71 9 76)(5 72 10 77)(11 110 16 105)(12 101 17 106)(13 102 18 107)(14 103 19 108)(15 104 20 109)(21 87 26 82)(22 88 27 83)(23 89 28 84)(24 90 29 85)(25 81 30 86)(31 63 36 68)(32 64 37 69)(33 65 38 70)(34 66 39 61)(35 67 40 62)(41 59 46 54)(42 60 47 55)(43 51 48 56)(44 52 49 57)(45 53 50 58)(91 151 96 156)(92 152 97 157)(93 153 98 158)(94 154 99 159)(95 155 100 160)(111 136 116 131)(112 137 117 132)(113 138 118 133)(114 139 119 134)(115 140 120 135)(121 146 126 141)(122 147 127 142)(123 148 128 143)(124 149 129 144)(125 150 130 145)
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), (1,145,24,133)(2,146,25,134)(3,147,26,135)(4,148,27,136)(5,149,28,137)(6,150,29,138)(7,141,30,139)(8,142,21,140)(9,143,22,131)(10,144,23,132)(11,33,153,45)(12,34,154,46)(13,35,155,47)(14,36,156,48)(15,37,157,49)(16,38,158,50)(17,39,159,41)(18,40,160,42)(19,31,151,43)(20,32,152,44)(51,103,63,91)(52,104,64,92)(53,105,65,93)(54,106,66,94)(55,107,67,95)(56,108,68,96)(57,109,69,97)(58,110,70,98)(59,101,61,99)(60,102,62,100)(71,123,83,111)(72,124,84,112)(73,125,85,113)(74,126,86,114)(75,127,87,115)(76,128,88,116)(77,129,89,117)(78,130,90,118)(79,121,81,119)(80,122,82,120), (2,10)(3,9)(4,8)(5,7)(11,158)(12,157)(13,156)(14,155)(15,154)(16,153)(17,152)(18,151)(19,160)(20,159)(21,27)(22,26)(23,25)(28,30)(31,35)(32,34)(36,40)(37,39)(41,49)(42,48)(43,47)(44,46)(51,55)(52,54)(56,60)(57,59)(61,69)(62,68)(63,67)(64,66)(71,75)(72,74)(76,80)(77,79)(81,89)(82,88)(83,87)(84,86)(91,102)(92,101)(93,110)(94,109)(95,108)(96,107)(97,106)(98,105)(99,104)(100,103)(111,122)(112,121)(113,130)(114,129)(115,128)(116,127)(117,126)(118,125)(119,124)(120,123)(131,142)(132,141)(133,150)(134,149)(135,148)(136,147)(137,146)(138,145)(139,144)(140,143), (1,65,24,53)(2,66,25,54)(3,67,26,55)(4,68,27,56)(5,69,28,57)(6,70,29,58)(7,61,30,59)(8,62,21,60)(9,63,22,51)(10,64,23,52)(11,113,153,125)(12,114,154,126)(13,115,155,127)(14,116,156,128)(15,117,157,129)(16,118,158,130)(17,119,159,121)(18,120,160,122)(19,111,151,123)(20,112,152,124)(31,71,43,83)(32,72,44,84)(33,73,45,85)(34,74,46,86)(35,75,47,87)(36,76,48,88)(37,77,49,89)(38,78,50,90)(39,79,41,81)(40,80,42,82)(91,131,103,143)(92,132,104,144)(93,133,105,145)(94,134,106,146)(95,135,107,147)(96,136,108,148)(97,137,109,149)(98,138,110,150)(99,139,101,141)(100,140,102,142), (1,78,6,73)(2,79,7,74)(3,80,8,75)(4,71,9,76)(5,72,10,77)(11,110,16,105)(12,101,17,106)(13,102,18,107)(14,103,19,108)(15,104,20,109)(21,87,26,82)(22,88,27,83)(23,89,28,84)(24,90,29,85)(25,81,30,86)(31,63,36,68)(32,64,37,69)(33,65,38,70)(34,66,39,61)(35,67,40,62)(41,59,46,54)(42,60,47,55)(43,51,48,56)(44,52,49,57)(45,53,50,58)(91,151,96,156)(92,152,97,157)(93,153,98,158)(94,154,99,159)(95,155,100,160)(111,136,116,131)(112,137,117,132)(113,138,118,133)(114,139,119,134)(115,140,120,135)(121,146,126,141)(122,147,127,142)(123,148,128,143)(124,149,129,144)(125,150,130,145)>;
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), (1,145,24,133)(2,146,25,134)(3,147,26,135)(4,148,27,136)(5,149,28,137)(6,150,29,138)(7,141,30,139)(8,142,21,140)(9,143,22,131)(10,144,23,132)(11,33,153,45)(12,34,154,46)(13,35,155,47)(14,36,156,48)(15,37,157,49)(16,38,158,50)(17,39,159,41)(18,40,160,42)(19,31,151,43)(20,32,152,44)(51,103,63,91)(52,104,64,92)(53,105,65,93)(54,106,66,94)(55,107,67,95)(56,108,68,96)(57,109,69,97)(58,110,70,98)(59,101,61,99)(60,102,62,100)(71,123,83,111)(72,124,84,112)(73,125,85,113)(74,126,86,114)(75,127,87,115)(76,128,88,116)(77,129,89,117)(78,130,90,118)(79,121,81,119)(80,122,82,120), (2,10)(3,9)(4,8)(5,7)(11,158)(12,157)(13,156)(14,155)(15,154)(16,153)(17,152)(18,151)(19,160)(20,159)(21,27)(22,26)(23,25)(28,30)(31,35)(32,34)(36,40)(37,39)(41,49)(42,48)(43,47)(44,46)(51,55)(52,54)(56,60)(57,59)(61,69)(62,68)(63,67)(64,66)(71,75)(72,74)(76,80)(77,79)(81,89)(82,88)(83,87)(84,86)(91,102)(92,101)(93,110)(94,109)(95,108)(96,107)(97,106)(98,105)(99,104)(100,103)(111,122)(112,121)(113,130)(114,129)(115,128)(116,127)(117,126)(118,125)(119,124)(120,123)(131,142)(132,141)(133,150)(134,149)(135,148)(136,147)(137,146)(138,145)(139,144)(140,143), (1,65,24,53)(2,66,25,54)(3,67,26,55)(4,68,27,56)(5,69,28,57)(6,70,29,58)(7,61,30,59)(8,62,21,60)(9,63,22,51)(10,64,23,52)(11,113,153,125)(12,114,154,126)(13,115,155,127)(14,116,156,128)(15,117,157,129)(16,118,158,130)(17,119,159,121)(18,120,160,122)(19,111,151,123)(20,112,152,124)(31,71,43,83)(32,72,44,84)(33,73,45,85)(34,74,46,86)(35,75,47,87)(36,76,48,88)(37,77,49,89)(38,78,50,90)(39,79,41,81)(40,80,42,82)(91,131,103,143)(92,132,104,144)(93,133,105,145)(94,134,106,146)(95,135,107,147)(96,136,108,148)(97,137,109,149)(98,138,110,150)(99,139,101,141)(100,140,102,142), (1,78,6,73)(2,79,7,74)(3,80,8,75)(4,71,9,76)(5,72,10,77)(11,110,16,105)(12,101,17,106)(13,102,18,107)(14,103,19,108)(15,104,20,109)(21,87,26,82)(22,88,27,83)(23,89,28,84)(24,90,29,85)(25,81,30,86)(31,63,36,68)(32,64,37,69)(33,65,38,70)(34,66,39,61)(35,67,40,62)(41,59,46,54)(42,60,47,55)(43,51,48,56)(44,52,49,57)(45,53,50,58)(91,151,96,156)(92,152,97,157)(93,153,98,158)(94,154,99,159)(95,155,100,160)(111,136,116,131)(112,137,117,132)(113,138,118,133)(114,139,119,134)(115,140,120,135)(121,146,126,141)(122,147,127,142)(123,148,128,143)(124,149,129,144)(125,150,130,145) );
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)], [(1,145,24,133),(2,146,25,134),(3,147,26,135),(4,148,27,136),(5,149,28,137),(6,150,29,138),(7,141,30,139),(8,142,21,140),(9,143,22,131),(10,144,23,132),(11,33,153,45),(12,34,154,46),(13,35,155,47),(14,36,156,48),(15,37,157,49),(16,38,158,50),(17,39,159,41),(18,40,160,42),(19,31,151,43),(20,32,152,44),(51,103,63,91),(52,104,64,92),(53,105,65,93),(54,106,66,94),(55,107,67,95),(56,108,68,96),(57,109,69,97),(58,110,70,98),(59,101,61,99),(60,102,62,100),(71,123,83,111),(72,124,84,112),(73,125,85,113),(74,126,86,114),(75,127,87,115),(76,128,88,116),(77,129,89,117),(78,130,90,118),(79,121,81,119),(80,122,82,120)], [(2,10),(3,9),(4,8),(5,7),(11,158),(12,157),(13,156),(14,155),(15,154),(16,153),(17,152),(18,151),(19,160),(20,159),(21,27),(22,26),(23,25),(28,30),(31,35),(32,34),(36,40),(37,39),(41,49),(42,48),(43,47),(44,46),(51,55),(52,54),(56,60),(57,59),(61,69),(62,68),(63,67),(64,66),(71,75),(72,74),(76,80),(77,79),(81,89),(82,88),(83,87),(84,86),(91,102),(92,101),(93,110),(94,109),(95,108),(96,107),(97,106),(98,105),(99,104),(100,103),(111,122),(112,121),(113,130),(114,129),(115,128),(116,127),(117,126),(118,125),(119,124),(120,123),(131,142),(132,141),(133,150),(134,149),(135,148),(136,147),(137,146),(138,145),(139,144),(140,143)], [(1,65,24,53),(2,66,25,54),(3,67,26,55),(4,68,27,56),(5,69,28,57),(6,70,29,58),(7,61,30,59),(8,62,21,60),(9,63,22,51),(10,64,23,52),(11,113,153,125),(12,114,154,126),(13,115,155,127),(14,116,156,128),(15,117,157,129),(16,118,158,130),(17,119,159,121),(18,120,160,122),(19,111,151,123),(20,112,152,124),(31,71,43,83),(32,72,44,84),(33,73,45,85),(34,74,46,86),(35,75,47,87),(36,76,48,88),(37,77,49,89),(38,78,50,90),(39,79,41,81),(40,80,42,82),(91,131,103,143),(92,132,104,144),(93,133,105,145),(94,134,106,146),(95,135,107,147),(96,136,108,148),(97,137,109,149),(98,138,110,150),(99,139,101,141),(100,140,102,142)], [(1,78,6,73),(2,79,7,74),(3,80,8,75),(4,71,9,76),(5,72,10,77),(11,110,16,105),(12,101,17,106),(13,102,18,107),(14,103,19,108),(15,104,20,109),(21,87,26,82),(22,88,27,83),(23,89,28,84),(24,90,29,85),(25,81,30,86),(31,63,36,68),(32,64,37,69),(33,65,38,70),(34,66,39,61),(35,67,40,62),(41,59,46,54),(42,60,47,55),(43,51,48,56),(44,52,49,57),(45,53,50,58),(91,151,96,156),(92,152,97,157),(93,153,98,158),(94,154,99,159),(95,155,100,160),(111,136,116,131),(112,137,117,132),(113,138,118,133),(114,139,119,134),(115,140,120,135),(121,146,126,141),(122,147,127,142),(123,148,128,143),(124,149,129,144),(125,150,130,145)]])
53 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | ··· | 4G | 4H | ··· | 4M | 4N | 4O | 4P | 4Q | 5A | 5B | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 20A | ··· | 20H | 20I | ··· | 20P |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 10 | 10 | 2 | 2 | 4 | ··· | 4 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
53 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | + | + | - | - | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D5 | C4○D4 | D10 | D10 | D10 | D10 | 2+ 1+4 | D4⋊2D5 | Q8×D5 | D4⋊8D10 |
| kernel | C10.1182+ 1+4 | Dic5.14D4 | Dic5⋊4D4 | C20⋊Q8 | Dic5.Q8 | D5×C4⋊C4 | D10⋊2Q8 | C2×C4⋊Dic5 | C4×C5⋊D4 | Q8×Dic5 | D10⋊3Q8 | C5×C22⋊Q8 | C5⋊D4 | C22⋊Q8 | C20 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C10 | C4 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 4 | 2 | 4 | 4 | 6 | 2 | 2 | 1 | 4 | 4 | 4 |
Matrix representation of C10.1182+ 1+4 ►in GL6(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 7 | 0 | 0 |
| 0 | 0 | 34 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 30 | 40 |
| 0 | 0 | 0 | 0 | 40 | 11 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 34 | 7 | 0 | 0 |
| 0 | 0 | 40 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 30 | 40 |
| 0 | 0 | 0 | 0 | 40 | 11 |
| 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 11 |
| 0 | 0 | 0 | 0 | 11 | 1 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,34,0,0,0,0,7,7,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[0,40,0,0,0,0,40,0,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,30,40,0,0,0,0,40,11],[1,0,0,0,0,0,0,40,0,0,0,0,0,0,34,40,0,0,0,0,7,7,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,30,40,0,0,0,0,40,11],[32,0,0,0,0,0,0,9,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,11,0,0,0,0,11,1] >;
C10.1182+ 1+4 in GAP, Magma, Sage, TeX
C_{10}._{118}2_+^{1+4} % in TeX
G:=Group("C10.118ES+(2,2)"); // GroupNames label
G:=SmallGroup(320,1307);
// by ID
G=gap.SmallGroup(320,1307);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,477,100,570,185,192,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=c^2=1,d^2=b^2,e^2=a^5,a*b=b*a,c*a*c=a^-1,a*d=d*a,a*e=e*a,c*b*c=a^5*b^-1,b*d=d*b,e*b*e^-1=a^5*b,c*d=d*c,c*e=e*c,e*d*e^-1=b^2*d>;
// generators/relations