G = C10.262- 1+4 order 320 = 26·5
26th non-split extension by C10 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.262- 1+4, C10.592+ 1+4, C22⋊Q8⋊24D5, C4⋊D20⋊28C2, C20⋊7D4⋊47C2, C4⋊C4.102D10, (C2×Q8).80D10, D10⋊D4⋊27C2, D10⋊3Q8⋊26C2, D10⋊2Q8⋊30C2, D10⋊Q8⋊25C2, C22⋊C4.24D10, C20.23D4⋊18C2, (C2×C20).177C23, (C2×C10).191C24, (C22×C4).253D10, C4⋊Dic5.48C22, D10.13D4⋊24C2, D10.12D4⋊28C2, C2.39(D4⋊8D10), C2.61(D4⋊6D10), Dic5.5D4⋊28C2, Dic5.Q8⋊23C2, (C2×D20).160C22, (Q8×C10).120C22, (C2×Dic5).97C23, (C22×D5).82C23, C23.127(C22×D5), C22.212(C23×D5), C23.D5.37C22, D10⋊C4.29C22, C23.23D10⋊14C2, (C22×C20).319C22, (C22×C10).219C23, C5⋊2(C22.56C24), (C4×Dic5).126C22, C10.D4.36C22, C2.27(Q8.10D10), (C2×Dic10).171C22, (C5×C22⋊Q8)⋊27C2, (C2×C4×D5).116C22, (C2×C4).57(C22×D5), (C5×C4⋊C4).171C22, (C2×C5⋊D4).43C22, (C5×C22⋊C4).46C22, SmallGroup(320,1319)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.262- 1+4
G = < a,b,c,d,e | a10=b4=c2=1, d2=b2, e2=a5b2, ab=ba, cac=dad-1=a-1, ae=ea, cbc=b-1, dbd-1=ebe-1=a5b, cd=dc, ece-1=a5c, ede-1=a5b2d >
Subgroups: 886 in 220 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, C4⋊D4, C22⋊Q8, C22⋊Q8, C22.D4, C4.4D4, C42.C2, Dic10, C4×D5, D20, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×Q8, C22×D5, C22×C10, C22.56C24, C4×Dic5, C10.D4, C4⋊Dic5, D10⋊C4, C23.D5, C5×C22⋊C4, C5×C4⋊C4, C2×Dic10, C2×C4×D5, C2×D20, C2×C5⋊D4, C22×C20, Q8×C10, D10.12D4, D10⋊D4, Dic5.5D4, Dic5.Q8, D10.13D4, C4⋊D20, D10⋊Q8, D10⋊2Q8, C23.23D10, C20⋊7D4, D10⋊3Q8, C20.23D4, C5×C22⋊Q8, C10.262- 1+4
Quotients: C1, C2, C22, C23, D5, C24, D10, 2+ 1+4, 2- 1+4, C22×D5, C22.56C24, C23×D5, D4⋊6D10, Q8.10D10, D4⋊8D10, C10.262- 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)
(1 118 18 103)(2 119 19 104)(3 120 20 105)(4 111 11 106)(5 112 12 107)(6 113 13 108)(7 114 14 109)(8 115 15 110)(9 116 16 101)(10 117 17 102)(21 96 36 81)(22 97 37 82)(23 98 38 83)(24 99 39 84)(25 100 40 85)(26 91 31 86)(27 92 32 87)(28 93 33 88)(29 94 34 89)(30 95 35 90)(41 156 56 141)(42 157 57 142)(43 158 58 143)(44 159 59 144)(45 160 60 145)(46 151 51 146)(47 152 52 147)(48 153 53 148)(49 154 54 149)(50 155 55 150)(61 136 76 121)(62 137 77 122)(63 138 78 123)(64 139 79 124)(65 140 80 125)(66 131 71 126)(67 132 72 127)(68 133 73 128)(69 134 74 129)(70 135 75 130)
(1 108)(2 107)(3 106)(4 105)(5 104)(6 103)(7 102)(8 101)(9 110)(10 109)(11 120)(12 119)(13 118)(14 117)(15 116)(16 115)(17 114)(18 113)(19 112)(20 111)(21 95)(22 94)(23 93)(24 92)(25 91)(26 100)(27 99)(28 98)(29 97)(30 96)(31 85)(32 84)(33 83)(34 82)(35 81)(36 90)(37 89)(38 88)(39 87)(40 86)(41 145)(42 144)(43 143)(44 142)(45 141)(46 150)(47 149)(48 148)(49 147)(50 146)(51 155)(52 154)(53 153)(54 152)(55 151)(56 160)(57 159)(58 158)(59 157)(60 156)(61 140)(62 139)(63 138)(64 137)(65 136)(66 135)(67 134)(68 133)(69 132)(70 131)(71 130)(72 129)(73 128)(74 127)(75 126)(76 125)(77 124)(78 123)(79 122)(80 121)
(1 48 18 53)(2 47 19 52)(3 46 20 51)(4 45 11 60)(5 44 12 59)(6 43 13 58)(7 42 14 57)(8 41 15 56)(9 50 16 55)(10 49 17 54)(21 75 36 70)(22 74 37 69)(23 73 38 68)(24 72 39 67)(25 71 40 66)(26 80 31 65)(27 79 32 64)(28 78 33 63)(29 77 34 62)(30 76 35 61)(81 140 96 125)(82 139 97 124)(83 138 98 123)(84 137 99 122)(85 136 100 121)(86 135 91 130)(87 134 92 129)(88 133 93 128)(89 132 94 127)(90 131 95 126)(101 145 116 160)(102 144 117 159)(103 143 118 158)(104 142 119 157)(105 141 120 156)(106 150 111 155)(107 149 112 154)(108 148 113 153)(109 147 114 152)(110 146 115 151)
(1 93 13 83)(2 94 14 84)(3 95 15 85)(4 96 16 86)(5 97 17 87)(6 98 18 88)(7 99 19 89)(8 100 20 90)(9 91 11 81)(10 92 12 82)(21 111 31 101)(22 112 32 102)(23 113 33 103)(24 114 34 104)(25 115 35 105)(26 116 36 106)(27 117 37 107)(28 118 38 108)(29 119 39 109)(30 120 40 110)(41 131 51 121)(42 132 52 122)(43 133 53 123)(44 134 54 124)(45 135 55 125)(46 136 56 126)(47 137 57 127)(48 138 58 128)(49 139 59 129)(50 140 60 130)(61 151 71 141)(62 152 72 142)(63 153 73 143)(64 154 74 144)(65 155 75 145)(66 156 76 146)(67 157 77 147)(68 158 78 148)(69 159 79 149)(70 160 80 150)
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), (1,118,18,103)(2,119,19,104)(3,120,20,105)(4,111,11,106)(5,112,12,107)(6,113,13,108)(7,114,14,109)(8,115,15,110)(9,116,16,101)(10,117,17,102)(21,96,36,81)(22,97,37,82)(23,98,38,83)(24,99,39,84)(25,100,40,85)(26,91,31,86)(27,92,32,87)(28,93,33,88)(29,94,34,89)(30,95,35,90)(41,156,56,141)(42,157,57,142)(43,158,58,143)(44,159,59,144)(45,160,60,145)(46,151,51,146)(47,152,52,147)(48,153,53,148)(49,154,54,149)(50,155,55,150)(61,136,76,121)(62,137,77,122)(63,138,78,123)(64,139,79,124)(65,140,80,125)(66,131,71,126)(67,132,72,127)(68,133,73,128)(69,134,74,129)(70,135,75,130), (1,108)(2,107)(3,106)(4,105)(5,104)(6,103)(7,102)(8,101)(9,110)(10,109)(11,120)(12,119)(13,118)(14,117)(15,116)(16,115)(17,114)(18,113)(19,112)(20,111)(21,95)(22,94)(23,93)(24,92)(25,91)(26,100)(27,99)(28,98)(29,97)(30,96)(31,85)(32,84)(33,83)(34,82)(35,81)(36,90)(37,89)(38,88)(39,87)(40,86)(41,145)(42,144)(43,143)(44,142)(45,141)(46,150)(47,149)(48,148)(49,147)(50,146)(51,155)(52,154)(53,153)(54,152)(55,151)(56,160)(57,159)(58,158)(59,157)(60,156)(61,140)(62,139)(63,138)(64,137)(65,136)(66,135)(67,134)(68,133)(69,132)(70,131)(71,130)(72,129)(73,128)(74,127)(75,126)(76,125)(77,124)(78,123)(79,122)(80,121), (1,48,18,53)(2,47,19,52)(3,46,20,51)(4,45,11,60)(5,44,12,59)(6,43,13,58)(7,42,14,57)(8,41,15,56)(9,50,16,55)(10,49,17,54)(21,75,36,70)(22,74,37,69)(23,73,38,68)(24,72,39,67)(25,71,40,66)(26,80,31,65)(27,79,32,64)(28,78,33,63)(29,77,34,62)(30,76,35,61)(81,140,96,125)(82,139,97,124)(83,138,98,123)(84,137,99,122)(85,136,100,121)(86,135,91,130)(87,134,92,129)(88,133,93,128)(89,132,94,127)(90,131,95,126)(101,145,116,160)(102,144,117,159)(103,143,118,158)(104,142,119,157)(105,141,120,156)(106,150,111,155)(107,149,112,154)(108,148,113,153)(109,147,114,152)(110,146,115,151), (1,93,13,83)(2,94,14,84)(3,95,15,85)(4,96,16,86)(5,97,17,87)(6,98,18,88)(7,99,19,89)(8,100,20,90)(9,91,11,81)(10,92,12,82)(21,111,31,101)(22,112,32,102)(23,113,33,103)(24,114,34,104)(25,115,35,105)(26,116,36,106)(27,117,37,107)(28,118,38,108)(29,119,39,109)(30,120,40,110)(41,131,51,121)(42,132,52,122)(43,133,53,123)(44,134,54,124)(45,135,55,125)(46,136,56,126)(47,137,57,127)(48,138,58,128)(49,139,59,129)(50,140,60,130)(61,151,71,141)(62,152,72,142)(63,153,73,143)(64,154,74,144)(65,155,75,145)(66,156,76,146)(67,157,77,147)(68,158,78,148)(69,159,79,149)(70,160,80,150)>;
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), (1,118,18,103)(2,119,19,104)(3,120,20,105)(4,111,11,106)(5,112,12,107)(6,113,13,108)(7,114,14,109)(8,115,15,110)(9,116,16,101)(10,117,17,102)(21,96,36,81)(22,97,37,82)(23,98,38,83)(24,99,39,84)(25,100,40,85)(26,91,31,86)(27,92,32,87)(28,93,33,88)(29,94,34,89)(30,95,35,90)(41,156,56,141)(42,157,57,142)(43,158,58,143)(44,159,59,144)(45,160,60,145)(46,151,51,146)(47,152,52,147)(48,153,53,148)(49,154,54,149)(50,155,55,150)(61,136,76,121)(62,137,77,122)(63,138,78,123)(64,139,79,124)(65,140,80,125)(66,131,71,126)(67,132,72,127)(68,133,73,128)(69,134,74,129)(70,135,75,130), (1,108)(2,107)(3,106)(4,105)(5,104)(6,103)(7,102)(8,101)(9,110)(10,109)(11,120)(12,119)(13,118)(14,117)(15,116)(16,115)(17,114)(18,113)(19,112)(20,111)(21,95)(22,94)(23,93)(24,92)(25,91)(26,100)(27,99)(28,98)(29,97)(30,96)(31,85)(32,84)(33,83)(34,82)(35,81)(36,90)(37,89)(38,88)(39,87)(40,86)(41,145)(42,144)(43,143)(44,142)(45,141)(46,150)(47,149)(48,148)(49,147)(50,146)(51,155)(52,154)(53,153)(54,152)(55,151)(56,160)(57,159)(58,158)(59,157)(60,156)(61,140)(62,139)(63,138)(64,137)(65,136)(66,135)(67,134)(68,133)(69,132)(70,131)(71,130)(72,129)(73,128)(74,127)(75,126)(76,125)(77,124)(78,123)(79,122)(80,121), (1,48,18,53)(2,47,19,52)(3,46,20,51)(4,45,11,60)(5,44,12,59)(6,43,13,58)(7,42,14,57)(8,41,15,56)(9,50,16,55)(10,49,17,54)(21,75,36,70)(22,74,37,69)(23,73,38,68)(24,72,39,67)(25,71,40,66)(26,80,31,65)(27,79,32,64)(28,78,33,63)(29,77,34,62)(30,76,35,61)(81,140,96,125)(82,139,97,124)(83,138,98,123)(84,137,99,122)(85,136,100,121)(86,135,91,130)(87,134,92,129)(88,133,93,128)(89,132,94,127)(90,131,95,126)(101,145,116,160)(102,144,117,159)(103,143,118,158)(104,142,119,157)(105,141,120,156)(106,150,111,155)(107,149,112,154)(108,148,113,153)(109,147,114,152)(110,146,115,151), (1,93,13,83)(2,94,14,84)(3,95,15,85)(4,96,16,86)(5,97,17,87)(6,98,18,88)(7,99,19,89)(8,100,20,90)(9,91,11,81)(10,92,12,82)(21,111,31,101)(22,112,32,102)(23,113,33,103)(24,114,34,104)(25,115,35,105)(26,116,36,106)(27,117,37,107)(28,118,38,108)(29,119,39,109)(30,120,40,110)(41,131,51,121)(42,132,52,122)(43,133,53,123)(44,134,54,124)(45,135,55,125)(46,136,56,126)(47,137,57,127)(48,138,58,128)(49,139,59,129)(50,140,60,130)(61,151,71,141)(62,152,72,142)(63,153,73,143)(64,154,74,144)(65,155,75,145)(66,156,76,146)(67,157,77,147)(68,158,78,148)(69,159,79,149)(70,160,80,150) );
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)], [(1,118,18,103),(2,119,19,104),(3,120,20,105),(4,111,11,106),(5,112,12,107),(6,113,13,108),(7,114,14,109),(8,115,15,110),(9,116,16,101),(10,117,17,102),(21,96,36,81),(22,97,37,82),(23,98,38,83),(24,99,39,84),(25,100,40,85),(26,91,31,86),(27,92,32,87),(28,93,33,88),(29,94,34,89),(30,95,35,90),(41,156,56,141),(42,157,57,142),(43,158,58,143),(44,159,59,144),(45,160,60,145),(46,151,51,146),(47,152,52,147),(48,153,53,148),(49,154,54,149),(50,155,55,150),(61,136,76,121),(62,137,77,122),(63,138,78,123),(64,139,79,124),(65,140,80,125),(66,131,71,126),(67,132,72,127),(68,133,73,128),(69,134,74,129),(70,135,75,130)], [(1,108),(2,107),(3,106),(4,105),(5,104),(6,103),(7,102),(8,101),(9,110),(10,109),(11,120),(12,119),(13,118),(14,117),(15,116),(16,115),(17,114),(18,113),(19,112),(20,111),(21,95),(22,94),(23,93),(24,92),(25,91),(26,100),(27,99),(28,98),(29,97),(30,96),(31,85),(32,84),(33,83),(34,82),(35,81),(36,90),(37,89),(38,88),(39,87),(40,86),(41,145),(42,144),(43,143),(44,142),(45,141),(46,150),(47,149),(48,148),(49,147),(50,146),(51,155),(52,154),(53,153),(54,152),(55,151),(56,160),(57,159),(58,158),(59,157),(60,156),(61,140),(62,139),(63,138),(64,137),(65,136),(66,135),(67,134),(68,133),(69,132),(70,131),(71,130),(72,129),(73,128),(74,127),(75,126),(76,125),(77,124),(78,123),(79,122),(80,121)], [(1,48,18,53),(2,47,19,52),(3,46,20,51),(4,45,11,60),(5,44,12,59),(6,43,13,58),(7,42,14,57),(8,41,15,56),(9,50,16,55),(10,49,17,54),(21,75,36,70),(22,74,37,69),(23,73,38,68),(24,72,39,67),(25,71,40,66),(26,80,31,65),(27,79,32,64),(28,78,33,63),(29,77,34,62),(30,76,35,61),(81,140,96,125),(82,139,97,124),(83,138,98,123),(84,137,99,122),(85,136,100,121),(86,135,91,130),(87,134,92,129),(88,133,93,128),(89,132,94,127),(90,131,95,126),(101,145,116,160),(102,144,117,159),(103,143,118,158),(104,142,119,157),(105,141,120,156),(106,150,111,155),(107,149,112,154),(108,148,113,153),(109,147,114,152),(110,146,115,151)], [(1,93,13,83),(2,94,14,84),(3,95,15,85),(4,96,16,86),(5,97,17,87),(6,98,18,88),(7,99,19,89),(8,100,20,90),(9,91,11,81),(10,92,12,82),(21,111,31,101),(22,112,32,102),(23,113,33,103),(24,114,34,104),(25,115,35,105),(26,116,36,106),(27,117,37,107),(28,118,38,108),(29,119,39,109),(30,120,40,110),(41,131,51,121),(42,132,52,122),(43,133,53,123),(44,134,54,124),(45,135,55,125),(46,136,56,126),(47,137,57,127),(48,138,58,128),(49,139,59,129),(50,140,60,130),(61,151,71,141),(62,152,72,142),(63,153,73,143),(64,154,74,144),(65,155,75,145),(66,156,76,146),(67,157,77,147),(68,158,78,148),(69,159,79,149),(70,160,80,150)]])
47 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4F | 4G | ··· | 4K | 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 | 5 | 5 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 4 | 20 | 20 | 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⋊8D10 |
| kernel | C10.262- 1+4 | D10.12D4 | D10⋊D4 | Dic5.5D4 | Dic5.Q8 | D10.13D4 | C4⋊D20 | D10⋊Q8 | D10⋊2Q8 | C23.23D10 | C20⋊7D4 | D10⋊3Q8 | C20.23D4 | C5×C22⋊Q8 | C22⋊Q8 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C10 | C10 | C2 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 4 | 6 | 2 | 2 | 2 | 1 | 4 | 4 | 4 |
Matrix representation of C10.262- 1+4 ►in GL8(𝔽41)
| 0 | 34 | 0 | 0 | 0 | 0 | 0 | 0 |
| 6 | 35 | 0 | 0 | 0 | 0 | 0 | 0 |
| 34 | 0 | 34 | 34 | 0 | 0 | 0 | 0 |
| 1 | 7 | 7 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 35 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 40 | 7 |
| 0 | 0 | 0 | 0 | 0 | 0 | 34 | 7 |
| 0 | 0 | 32 | 9 | 0 | 0 | 0 | 0 |
| 19 | 32 | 23 | 19 | 0 | 0 | 0 | 0 |
| 14 | 2 | 9 | 0 | 0 | 0 | 0 | 0 |
| 5 | 2 | 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 34 | 22 | 19 |
| 0 | 0 | 0 | 0 | 6 | 14 | 0 | 13 |
| 0 | 0 | 0 | 0 | 5 | 14 | 26 | 7 |
| 0 | 0 | 0 | 0 | 34 | 7 | 34 | 34 |
| 22 | 9 | 31 | 9 | 0 | 0 | 0 | 0 |
| 32 | 28 | 28 | 19 | 0 | 0 | 0 | 0 |
| 27 | 39 | 32 | 0 | 0 | 0 | 0 | 0 |
| 40 | 7 | 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 15 | 9 | 0 |
| 0 | 0 | 0 | 0 | 6 | 33 | 13 | 32 |
| 0 | 0 | 0 | 0 | 24 | 0 | 25 | 15 |
| 0 | 0 | 0 | 0 | 21 | 17 | 26 | 16 |
| 5 | 30 | 3 | 21 | 0 | 0 | 0 | 0 |
| 30 | 16 | 3 | 18 | 0 | 0 | 0 | 0 |
| 9 | 0 | 11 | 9 | 0 | 0 | 0 | 0 |
| 25 | 11 | 11 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 29 | 40 | 12 |
| 0 | 0 | 0 | 0 | 2 | 28 | 6 | 30 |
| 0 | 0 | 0 | 0 | 14 | 19 | 23 | 12 |
| 0 | 0 | 0 | 0 | 30 | 5 | 9 | 18 |
| 32 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 32 | 0 | 0 | 0 | 0 | 0 | 0 |
| 14 | 2 | 9 | 0 | 0 | 0 | 0 | 0 |
| 14 | 2 | 0 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 30 | 14 | 14 |
| 0 | 0 | 0 | 0 | 27 | 0 | 13 | 16 |
| 0 | 0 | 0 | 0 | 4 | 1 | 16 | 11 |
| 0 | 0 | 0 | 0 | 9 | 10 | 30 | 11 |
G:=sub<GL(8,GF(41))| [0,6,34,1,0,0,0,0,34,35,0,7,0,0,0,0,0,0,34,7,0,0,0,0,0,0,34,1,0,0,0,0,0,0,0,0,6,35,0,0,0,0,0,0,7,0,0,0,0,0,0,0,0,0,40,34,0,0,0,0,0,0,7,7],[0,19,14,5,0,0,0,0,0,32,2,2,0,0,0,0,32,23,9,9,0,0,0,0,9,19,0,0,0,0,0,0,0,0,0,0,8,6,5,34,0,0,0,0,34,14,14,7,0,0,0,0,22,0,26,34,0,0,0,0,19,13,7,34],[22,32,27,40,0,0,0,0,9,28,39,7,0,0,0,0,31,28,32,32,0,0,0,0,9,19,0,0,0,0,0,0,0,0,0,0,8,6,24,21,0,0,0,0,15,33,0,17,0,0,0,0,9,13,25,26,0,0,0,0,0,32,15,16],[5,30,9,25,0,0,0,0,30,16,0,11,0,0,0,0,3,3,11,11,0,0,0,0,21,18,9,9,0,0,0,0,0,0,0,0,13,2,14,30,0,0,0,0,29,28,19,5,0,0,0,0,40,6,23,9,0,0,0,0,12,30,12,18],[32,0,14,14,0,0,0,0,0,32,2,2,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,14,27,4,9,0,0,0,0,30,0,1,10,0,0,0,0,14,13,16,30,0,0,0,0,14,16,11,11] >;
C10.262- 1+4 in GAP, Magma, Sage, TeX
C_{10}._{26}2_-^{1+4} % in TeX
G:=Group("C10.26ES-(2,2)"); // GroupNames label
G:=SmallGroup(320,1319);
// by ID
G=gap.SmallGroup(320,1319);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,120,758,219,100,1571,570,12550]);
// 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,a*b=b*a,c*a*c=d*a*d^-1=a^-1,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=a^5*b^2*d>;
// generators/relations