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G = C10.262- 1+4order 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⋊Q824D5, C4⋊D2028C2, C207D447C2, C4⋊C4.102D10, (C2×Q8).80D10, D10⋊D427C2, D103Q826C2, D102Q830C2, D10⋊Q825C2, C22⋊C4.24D10, C20.23D418C2, (C2×C20).177C23, (C2×C10).191C24, (C22×C4).253D10, C4⋊Dic5.48C22, D10.13D424C2, D10.12D428C2, C2.39(D48D10), C2.61(D46D10), Dic5.5D428C2, Dic5.Q823C2, (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, C23.23D1014C2, (C22×C20).319C22, (C22×C10).219C23, C52(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

C1C2×C10 — C10.262- 1+4
C1C5C10C2×C10C22×D5C2×C4×D5D103Q8 — C10.262- 1+4
C5C2×C10 — C10.262- 1+4
C1C22C22⋊Q8

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 [×3], C2 [×4], C4 [×11], C22, C22 [×12], C5, C2×C4 [×6], C2×C4 [×9], D4 [×6], Q8 [×2], C23, C23 [×3], D5 [×3], C10 [×3], C10, C42, C22⋊C4 [×2], C22⋊C4 [×10], C4⋊C4 [×3], C4⋊C4 [×7], C22×C4, C22×C4 [×3], C2×D4 [×6], C2×Q8, C2×Q8, Dic5 [×5], C20 [×6], D10 [×9], C2×C10, C2×C10 [×3], C4⋊D4 [×4], C22⋊Q8, C22⋊Q8 [×3], C22.D4 [×4], C4.4D4 [×2], C42.C2, Dic10, C4×D5 [×3], D20 [×3], C2×Dic5 [×5], C5⋊D4 [×3], C2×C20 [×6], C2×C20, C5×Q8, C22×D5 [×3], C22×C10, C22.56C24, C4×Dic5, C10.D4 [×5], C4⋊Dic5 [×2], D10⋊C4 [×9], C23.D5, C5×C22⋊C4 [×2], C5×C4⋊C4 [×3], C2×Dic10, C2×C4×D5 [×3], C2×D20 [×3], C2×C5⋊D4 [×3], C22×C20, Q8×C10, D10.12D4, D10⋊D4 [×2], Dic5.5D4, Dic5.Q8, D10.13D4 [×2], C4⋊D20, D10⋊Q8, D102Q8, C23.23D10, C207D4, D103Q8, C20.23D4, C5×C22⋊Q8, C10.262- 1+4
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], D5, C24, D10 [×7], 2+ 1+4 [×2], 2- 1+4, C22×D5 [×7], C22.56C24, C23×D5, D46D10, Q8.10D10, D48D10, C10.262- 1+4

Smallest permutation representation of 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 2A2B2C2D2E2F2G4A···4F4G···4K5A5B10A···10F10G10H10I10J20A···20H20I···20P
order122222224···44···45510···101010101020···2020···20
size111142020204···420···20222···244444···48···8

47 irreducible representations

dim111111111111112222244444
type++++++++++++++++++++-+
imageC1C2C2C2C2C2C2C2C2C2C2C2C2C2D5D10D10D10D102+ 1+42- 1+4D46D10Q8.10D10D48D10
kernelC10.262- 1+4D10.12D4D10⋊D4Dic5.5D4Dic5.Q8D10.13D4C4⋊D20D10⋊Q8D102Q8C23.23D10C207D4D103Q8C20.23D4C5×C22⋊Q8C22⋊Q8C22⋊C4C4⋊C4C22×C4C2×Q8C10C10C2C2C2
# reps112112111111112462221444

Matrix representation of C10.262- 1+4 in GL8(𝔽41)

034000000
635000000
34034340000
17710000
00006700
000035000
000000407
000000347
,
003290000
193223190000
142900000
52900000
00008342219
0000614013
0000514267
00003473434
,
2293190000
322828190000
27393200000
4073200000
000081590
00006331332
00002402515
000021172616
,
5303210000
30163180000
901190000
25111190000
000013294012
0000228630
000014192312
0000305918
,
320000000
032000000
142900000
142090000
000014301414
00002701316
0000411611
00009103011

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

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