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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

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C10 — C10.262- 1+4
 Chief series C1 — C5 — C10 — C2×C10 — C22×D5 — C2×C4×D5 — D10⋊3Q8 — C10.262- 1+4
 Lower central C5 — C2×C10 — C10.262- 1+4
 Upper central C1 — C22 — C22⋊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, 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, D102Q8, C23.23D10, C207D4, D103Q8, 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, 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 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`

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