G = C10.242- 1+4 order 320 = 26·5
24th non-split extension by C10 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.242- 1+4, C10.1192+ 1+4, C20⋊Q8⋊28C2, C4⋊C4.99D10, C22⋊Q8⋊20D5, (Q8×Dic5)⋊17C2, D20⋊8C4⋊30C2, D10⋊2Q8⋊29C2, C20⋊7D4.16C2, (C2×Q8).133D10, C22⋊C4.22D10, C20.214(C4○D4), C20.23D4⋊16C2, C4.73(D4⋊2D5), (C2×C20).175C23, (C2×C10).187C24, (C22×C4).249D10, D10.12D4⋊27C2, C2.37(D4⋊8D10), Dic5.5D4⋊27C2, (C2×D20).159C22, C4⋊Dic5.312C22, (Q8×C10).117C22, (C2×Dic5).94C23, (C22×D5).78C23, C22.208(C23×D5), C23.125(C22×D5), D10⋊C4.28C22, C23.21D10⋊31C2, (C22×C20).262C22, (C22×C10).215C23, C5⋊6(C22.36C24), (C4×Dic5).123C22, C10.D4.35C22, C23.D5.126C22, C2.25(Q8.10D10), (C2×Dic10).170C22, C4⋊C4⋊D5⋊22C2, C10.91(C2×C4○D4), (C5×C22⋊Q8)⋊23C2, C2.50(C2×D4⋊2D5), (C2×C4×D5).113C22, (C5×C4⋊C4).168C22, (C2×C4).593(C22×D5), (C2×C5⋊D4).39C22, (C5×C22⋊C4).42C22, SmallGroup(320,1315)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.242- 1+4
G = < a,b,c,d,e | a10=b4=c2=1, d2=b2, e2=a5b2, bab-1=cac=a-1, ad=da, ae=ea, cbc=b-1, dbd-1=ebe-1=a5b, cd=dc, ece-1=a5c, ede-1=b2d >
Subgroups: 766 in 216 conjugacy classes, 95 normal (43 characteristic)
C1, C2, C2, C4, C4, 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, C20, C20, D10, C2×C10, C2×C10, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22⋊Q8, C22.D4, C4.4D4, C42⋊2C2, C4⋊Q8, Dic10, C4×D5, D20, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C2×C20, C5×Q8, C22×D5, C22×C10, C22.36C24, C4×Dic5, C4×Dic5, C10.D4, C4⋊Dic5, C4⋊Dic5, D10⋊C4, C23.D5, C5×C22⋊C4, C5×C4⋊C4, C5×C4⋊C4, C2×Dic10, C2×C4×D5, C2×D20, C2×C5⋊D4, C22×C20, Q8×C10, D10.12D4, Dic5.5D4, C20⋊Q8, D20⋊8C4, D10⋊2Q8, C4⋊C4⋊D5, C23.21D10, C20⋊7D4, Q8×Dic5, C20.23D4, C5×C22⋊Q8, C10.242- 1+4
Quotients: C1, C2, C22, C23, D5, C4○D4, C24, D10, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D5, C22.36C24, D4⋊2D5, C23×D5, C2×D4⋊2D5, Q8.10D10, D4⋊8D10, C10.242- 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 40 30 50)(2 39 21 49)(3 38 22 48)(4 37 23 47)(5 36 24 46)(6 35 25 45)(7 34 26 44)(8 33 27 43)(9 32 28 42)(10 31 29 41)(11 135 155 145)(12 134 156 144)(13 133 157 143)(14 132 158 142)(15 131 159 141)(16 140 160 150)(17 139 151 149)(18 138 152 148)(19 137 153 147)(20 136 154 146)(51 89 61 79)(52 88 62 78)(53 87 63 77)(54 86 64 76)(55 85 65 75)(56 84 66 74)(57 83 67 73)(58 82 68 72)(59 81 69 71)(60 90 70 80)(91 129 101 119)(92 128 102 118)(93 127 103 117)(94 126 104 116)(95 125 105 115)(96 124 106 114)(97 123 107 113)(98 122 108 112)(99 121 109 111)(100 130 110 120)
(1 80)(2 79)(3 78)(4 77)(5 76)(6 75)(7 74)(8 73)(9 72)(10 71)(11 100)(12 99)(13 98)(14 97)(15 96)(16 95)(17 94)(18 93)(19 92)(20 91)(21 89)(22 88)(23 87)(24 86)(25 85)(26 84)(27 83)(28 82)(29 81)(30 90)(31 69)(32 68)(33 67)(34 66)(35 65)(36 64)(37 63)(38 62)(39 61)(40 70)(41 59)(42 58)(43 57)(44 56)(45 55)(46 54)(47 53)(48 52)(49 51)(50 60)(101 154)(102 153)(103 152)(104 151)(105 160)(106 159)(107 158)(108 157)(109 156)(110 155)(111 134)(112 133)(113 132)(114 131)(115 140)(116 139)(117 138)(118 137)(119 136)(120 135)(121 144)(122 143)(123 142)(124 141)(125 150)(126 149)(127 148)(128 147)(129 146)(130 145)
(1 155 30 11)(2 156 21 12)(3 157 22 13)(4 158 23 14)(5 159 24 15)(6 160 25 16)(7 151 26 17)(8 152 27 18)(9 153 28 19)(10 154 29 20)(31 141 41 131)(32 142 42 132)(33 143 43 133)(34 144 44 134)(35 145 45 135)(36 146 46 136)(37 147 47 137)(38 148 48 138)(39 149 49 139)(40 150 50 140)(51 116 61 126)(52 117 62 127)(53 118 63 128)(54 119 64 129)(55 120 65 130)(56 111 66 121)(57 112 67 122)(58 113 68 123)(59 114 69 124)(60 115 70 125)(71 101 81 91)(72 102 82 92)(73 103 83 93)(74 104 84 94)(75 105 85 95)(76 106 86 96)(77 107 87 97)(78 108 88 98)(79 109 89 99)(80 110 90 100)
(1 50 25 35)(2 41 26 36)(3 42 27 37)(4 43 28 38)(5 44 29 39)(6 45 30 40)(7 46 21 31)(8 47 22 32)(9 48 23 33)(10 49 24 34)(11 140 160 145)(12 131 151 146)(13 132 152 147)(14 133 153 148)(15 134 154 149)(16 135 155 150)(17 136 156 141)(18 137 157 142)(19 138 158 143)(20 139 159 144)(51 81 66 76)(52 82 67 77)(53 83 68 78)(54 84 69 79)(55 85 70 80)(56 86 61 71)(57 87 62 72)(58 88 63 73)(59 89 64 74)(60 90 65 75)(91 111 106 126)(92 112 107 127)(93 113 108 128)(94 114 109 129)(95 115 110 130)(96 116 101 121)(97 117 102 122)(98 118 103 123)(99 119 104 124)(100 120 105 125)
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), (1,40,30,50)(2,39,21,49)(3,38,22,48)(4,37,23,47)(5,36,24,46)(6,35,25,45)(7,34,26,44)(8,33,27,43)(9,32,28,42)(10,31,29,41)(11,135,155,145)(12,134,156,144)(13,133,157,143)(14,132,158,142)(15,131,159,141)(16,140,160,150)(17,139,151,149)(18,138,152,148)(19,137,153,147)(20,136,154,146)(51,89,61,79)(52,88,62,78)(53,87,63,77)(54,86,64,76)(55,85,65,75)(56,84,66,74)(57,83,67,73)(58,82,68,72)(59,81,69,71)(60,90,70,80)(91,129,101,119)(92,128,102,118)(93,127,103,117)(94,126,104,116)(95,125,105,115)(96,124,106,114)(97,123,107,113)(98,122,108,112)(99,121,109,111)(100,130,110,120), (1,80)(2,79)(3,78)(4,77)(5,76)(6,75)(7,74)(8,73)(9,72)(10,71)(11,100)(12,99)(13,98)(14,97)(15,96)(16,95)(17,94)(18,93)(19,92)(20,91)(21,89)(22,88)(23,87)(24,86)(25,85)(26,84)(27,83)(28,82)(29,81)(30,90)(31,69)(32,68)(33,67)(34,66)(35,65)(36,64)(37,63)(38,62)(39,61)(40,70)(41,59)(42,58)(43,57)(44,56)(45,55)(46,54)(47,53)(48,52)(49,51)(50,60)(101,154)(102,153)(103,152)(104,151)(105,160)(106,159)(107,158)(108,157)(109,156)(110,155)(111,134)(112,133)(113,132)(114,131)(115,140)(116,139)(117,138)(118,137)(119,136)(120,135)(121,144)(122,143)(123,142)(124,141)(125,150)(126,149)(127,148)(128,147)(129,146)(130,145), (1,155,30,11)(2,156,21,12)(3,157,22,13)(4,158,23,14)(5,159,24,15)(6,160,25,16)(7,151,26,17)(8,152,27,18)(9,153,28,19)(10,154,29,20)(31,141,41,131)(32,142,42,132)(33,143,43,133)(34,144,44,134)(35,145,45,135)(36,146,46,136)(37,147,47,137)(38,148,48,138)(39,149,49,139)(40,150,50,140)(51,116,61,126)(52,117,62,127)(53,118,63,128)(54,119,64,129)(55,120,65,130)(56,111,66,121)(57,112,67,122)(58,113,68,123)(59,114,69,124)(60,115,70,125)(71,101,81,91)(72,102,82,92)(73,103,83,93)(74,104,84,94)(75,105,85,95)(76,106,86,96)(77,107,87,97)(78,108,88,98)(79,109,89,99)(80,110,90,100), (1,50,25,35)(2,41,26,36)(3,42,27,37)(4,43,28,38)(5,44,29,39)(6,45,30,40)(7,46,21,31)(8,47,22,32)(9,48,23,33)(10,49,24,34)(11,140,160,145)(12,131,151,146)(13,132,152,147)(14,133,153,148)(15,134,154,149)(16,135,155,150)(17,136,156,141)(18,137,157,142)(19,138,158,143)(20,139,159,144)(51,81,66,76)(52,82,67,77)(53,83,68,78)(54,84,69,79)(55,85,70,80)(56,86,61,71)(57,87,62,72)(58,88,63,73)(59,89,64,74)(60,90,65,75)(91,111,106,126)(92,112,107,127)(93,113,108,128)(94,114,109,129)(95,115,110,130)(96,116,101,121)(97,117,102,122)(98,118,103,123)(99,119,104,124)(100,120,105,125)>;
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), (1,40,30,50)(2,39,21,49)(3,38,22,48)(4,37,23,47)(5,36,24,46)(6,35,25,45)(7,34,26,44)(8,33,27,43)(9,32,28,42)(10,31,29,41)(11,135,155,145)(12,134,156,144)(13,133,157,143)(14,132,158,142)(15,131,159,141)(16,140,160,150)(17,139,151,149)(18,138,152,148)(19,137,153,147)(20,136,154,146)(51,89,61,79)(52,88,62,78)(53,87,63,77)(54,86,64,76)(55,85,65,75)(56,84,66,74)(57,83,67,73)(58,82,68,72)(59,81,69,71)(60,90,70,80)(91,129,101,119)(92,128,102,118)(93,127,103,117)(94,126,104,116)(95,125,105,115)(96,124,106,114)(97,123,107,113)(98,122,108,112)(99,121,109,111)(100,130,110,120), (1,80)(2,79)(3,78)(4,77)(5,76)(6,75)(7,74)(8,73)(9,72)(10,71)(11,100)(12,99)(13,98)(14,97)(15,96)(16,95)(17,94)(18,93)(19,92)(20,91)(21,89)(22,88)(23,87)(24,86)(25,85)(26,84)(27,83)(28,82)(29,81)(30,90)(31,69)(32,68)(33,67)(34,66)(35,65)(36,64)(37,63)(38,62)(39,61)(40,70)(41,59)(42,58)(43,57)(44,56)(45,55)(46,54)(47,53)(48,52)(49,51)(50,60)(101,154)(102,153)(103,152)(104,151)(105,160)(106,159)(107,158)(108,157)(109,156)(110,155)(111,134)(112,133)(113,132)(114,131)(115,140)(116,139)(117,138)(118,137)(119,136)(120,135)(121,144)(122,143)(123,142)(124,141)(125,150)(126,149)(127,148)(128,147)(129,146)(130,145), (1,155,30,11)(2,156,21,12)(3,157,22,13)(4,158,23,14)(5,159,24,15)(6,160,25,16)(7,151,26,17)(8,152,27,18)(9,153,28,19)(10,154,29,20)(31,141,41,131)(32,142,42,132)(33,143,43,133)(34,144,44,134)(35,145,45,135)(36,146,46,136)(37,147,47,137)(38,148,48,138)(39,149,49,139)(40,150,50,140)(51,116,61,126)(52,117,62,127)(53,118,63,128)(54,119,64,129)(55,120,65,130)(56,111,66,121)(57,112,67,122)(58,113,68,123)(59,114,69,124)(60,115,70,125)(71,101,81,91)(72,102,82,92)(73,103,83,93)(74,104,84,94)(75,105,85,95)(76,106,86,96)(77,107,87,97)(78,108,88,98)(79,109,89,99)(80,110,90,100), (1,50,25,35)(2,41,26,36)(3,42,27,37)(4,43,28,38)(5,44,29,39)(6,45,30,40)(7,46,21,31)(8,47,22,32)(9,48,23,33)(10,49,24,34)(11,140,160,145)(12,131,151,146)(13,132,152,147)(14,133,153,148)(15,134,154,149)(16,135,155,150)(17,136,156,141)(18,137,157,142)(19,138,158,143)(20,139,159,144)(51,81,66,76)(52,82,67,77)(53,83,68,78)(54,84,69,79)(55,85,70,80)(56,86,61,71)(57,87,62,72)(58,88,63,73)(59,89,64,74)(60,90,65,75)(91,111,106,126)(92,112,107,127)(93,113,108,128)(94,114,109,129)(95,115,110,130)(96,116,101,121)(97,117,102,122)(98,118,103,123)(99,119,104,124)(100,120,105,125) );
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)], [(1,40,30,50),(2,39,21,49),(3,38,22,48),(4,37,23,47),(5,36,24,46),(6,35,25,45),(7,34,26,44),(8,33,27,43),(9,32,28,42),(10,31,29,41),(11,135,155,145),(12,134,156,144),(13,133,157,143),(14,132,158,142),(15,131,159,141),(16,140,160,150),(17,139,151,149),(18,138,152,148),(19,137,153,147),(20,136,154,146),(51,89,61,79),(52,88,62,78),(53,87,63,77),(54,86,64,76),(55,85,65,75),(56,84,66,74),(57,83,67,73),(58,82,68,72),(59,81,69,71),(60,90,70,80),(91,129,101,119),(92,128,102,118),(93,127,103,117),(94,126,104,116),(95,125,105,115),(96,124,106,114),(97,123,107,113),(98,122,108,112),(99,121,109,111),(100,130,110,120)], [(1,80),(2,79),(3,78),(4,77),(5,76),(6,75),(7,74),(8,73),(9,72),(10,71),(11,100),(12,99),(13,98),(14,97),(15,96),(16,95),(17,94),(18,93),(19,92),(20,91),(21,89),(22,88),(23,87),(24,86),(25,85),(26,84),(27,83),(28,82),(29,81),(30,90),(31,69),(32,68),(33,67),(34,66),(35,65),(36,64),(37,63),(38,62),(39,61),(40,70),(41,59),(42,58),(43,57),(44,56),(45,55),(46,54),(47,53),(48,52),(49,51),(50,60),(101,154),(102,153),(103,152),(104,151),(105,160),(106,159),(107,158),(108,157),(109,156),(110,155),(111,134),(112,133),(113,132),(114,131),(115,140),(116,139),(117,138),(118,137),(119,136),(120,135),(121,144),(122,143),(123,142),(124,141),(125,150),(126,149),(127,148),(128,147),(129,146),(130,145)], [(1,155,30,11),(2,156,21,12),(3,157,22,13),(4,158,23,14),(5,159,24,15),(6,160,25,16),(7,151,26,17),(8,152,27,18),(9,153,28,19),(10,154,29,20),(31,141,41,131),(32,142,42,132),(33,143,43,133),(34,144,44,134),(35,145,45,135),(36,146,46,136),(37,147,47,137),(38,148,48,138),(39,149,49,139),(40,150,50,140),(51,116,61,126),(52,117,62,127),(53,118,63,128),(54,119,64,129),(55,120,65,130),(56,111,66,121),(57,112,67,122),(58,113,68,123),(59,114,69,124),(60,115,70,125),(71,101,81,91),(72,102,82,92),(73,103,83,93),(74,104,84,94),(75,105,85,95),(76,106,86,96),(77,107,87,97),(78,108,88,98),(79,109,89,99),(80,110,90,100)], [(1,50,25,35),(2,41,26,36),(3,42,27,37),(4,43,28,38),(5,44,29,39),(6,45,30,40),(7,46,21,31),(8,47,22,32),(9,48,23,33),(10,49,24,34),(11,140,160,145),(12,131,151,146),(13,132,152,147),(14,133,153,148),(15,134,154,149),(16,135,155,150),(17,136,156,141),(18,137,157,142),(19,138,158,143),(20,139,159,144),(51,81,66,76),(52,82,67,77),(53,83,68,78),(54,84,69,79),(55,85,70,80),(56,86,61,71),(57,87,62,72),(58,88,63,73),(59,89,64,74),(60,90,65,75),(91,111,106,126),(92,112,107,127),(93,113,108,128),(94,114,109,129),(95,115,110,130),(96,116,101,121),(97,117,102,122),(98,118,103,123),(99,119,104,124),(100,120,105,125)]])
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | ··· | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 5A | 5B | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 20A | ··· | 20H | 20I | ··· | 20P |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 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 | 4 | 20 | 20 | 2 | 2 | 4 | ··· | 4 | 10 | 10 | 10 | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
50 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D5 | C4○D4 | D10 | D10 | D10 | D10 | 2+ 1+4 | 2- 1+4 | D4⋊2D5 | Q8.10D10 | D4⋊8D10 |
| kernel | C10.242- 1+4 | D10.12D4 | Dic5.5D4 | C20⋊Q8 | D20⋊8C4 | D10⋊2Q8 | C4⋊C4⋊D5 | C23.21D10 | C20⋊7D4 | Q8×Dic5 | C20.23D4 | C5×C22⋊Q8 | C22⋊Q8 | C20 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C10 | C10 | C4 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 4 | 4 | 6 | 2 | 2 | 1 | 1 | 4 | 4 | 4 |
Matrix representation of C10.242- 1+4 ►in GL8(𝔽41)
| 0 | 6 | 0 | 0 | 0 | 0 | 0 | 0 |
| 34 | 7 | 0 | 0 | 0 | 0 | 0 | 0 |
| 35 | 0 | 6 | 6 | 0 | 0 | 0 | 0 |
| 40 | 6 | 35 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 6 | 0 | 0 |
| 0 | 0 | 0 | 0 | 34 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 39 | 39 | 7 | 6 |
| 0 | 0 | 0 | 0 | 0 | 2 | 34 | 0 |
| 6 | 40 | 36 | 1 | 0 | 0 | 0 | 0 |
| 1 | 34 | 7 | 6 | 0 | 0 | 0 | 0 |
| 38 | 21 | 1 | 0 | 0 | 0 | 0 | 0 |
| 31 | 22 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 25 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 14 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 9 | 27 | 25 |
| 0 | 0 | 0 | 0 | 26 | 20 | 25 | 14 |
| 7 | 40 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7 | 34 | 0 | 0 | 0 | 0 | 0 | 0 |
| 38 | 21 | 1 | 0 | 0 | 0 | 0 | 0 |
| 32 | 22 | 6 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 9 | 13 | 9 |
| 0 | 0 | 0 | 0 | 26 | 7 | 9 | 28 |
| 0 | 0 | 0 | 0 | 33 | 3 | 34 | 9 |
| 0 | 0 | 0 | 0 | 15 | 8 | 26 | 33 |
| 5 | 6 | 12 | 12 | 0 | 0 | 0 | 0 |
| 20 | 24 | 0 | 14 | 0 | 0 | 0 | 0 |
| 40 | 6 | 18 | 35 | 0 | 0 | 0 | 0 |
| 23 | 0 | 18 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 38 | 24 | 6 |
| 0 | 0 | 0 | 0 | 16 | 40 | 34 | 17 |
| 0 | 0 | 0 | 0 | 8 | 37 | 17 | 1 |
| 0 | 0 | 0 | 0 | 39 | 6 | 25 | 3 |
| 0 | 0 | 1 | 40 | 0 | 0 | 0 | 0 |
| 6 | 40 | 2 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 40 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 30 | 0 | 0 |
| 0 | 0 | 0 | 0 | 23 | 23 | 11 | 13 |
| 0 | 0 | 0 | 0 | 0 | 18 | 19 | 30 |
G:=sub<GL(8,GF(41))| [0,34,35,40,0,0,0,0,6,7,0,6,0,0,0,0,0,0,6,35,0,0,0,0,0,0,6,1,0,0,0,0,0,0,0,0,7,34,39,0,0,0,0,0,6,0,39,2,0,0,0,0,0,0,7,34,0,0,0,0,0,0,6,0],[6,1,38,31,0,0,0,0,40,34,21,22,0,0,0,0,36,7,1,1,0,0,0,0,1,6,0,0,0,0,0,0,0,0,0,0,27,25,21,26,0,0,0,0,25,14,9,20,0,0,0,0,0,0,27,25,0,0,0,0,0,0,25,14],[7,7,38,32,0,0,0,0,40,34,21,22,0,0,0,0,0,0,1,6,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,8,26,33,15,0,0,0,0,9,7,3,8,0,0,0,0,13,9,34,26,0,0,0,0,9,28,9,33],[5,20,40,23,0,0,0,0,6,24,6,0,0,0,0,0,12,0,18,18,0,0,0,0,12,14,35,35,0,0,0,0,0,0,0,0,22,16,8,39,0,0,0,0,38,40,37,6,0,0,0,0,24,34,17,25,0,0,0,0,6,17,1,3],[0,6,0,40,0,0,0,0,0,40,0,0,0,0,0,0,1,2,1,1,0,0,0,0,40,35,0,0,0,0,0,0,0,0,0,0,11,19,23,0,0,0,0,0,13,30,23,18,0,0,0,0,0,0,11,19,0,0,0,0,0,0,13,30] >;
C10.242- 1+4 in GAP, Magma, Sage, TeX
C_{10}._{24}2_-^{1+4} % in TeX
G:=Group("C10.24ES-(2,2)"); // GroupNames label
G:=SmallGroup(320,1315);
// by ID
G=gap.SmallGroup(320,1315);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,758,219,675,570,192,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=c^2=1,d^2=b^2,e^2=a^5*b^2,b*a*b^-1=c*a*c=a^-1,a*d=d*a,a*e=e*a,c*b*c=b^-1,d*b*d^-1=e*b*e^-1=a^5*b,c*d=d*c,e*c*e^-1=a^5*c,e*d*e^-1=b^2*d>;
// generators/relations