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## G = C10.742- 1+4order 320 = 26·5

### 29th non-split extension by C10 of 2- 1+4 acting via 2- 1+4/C4○D4=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C10 — C10.742- 1+4
 Chief series C1 — C5 — C10 — C2×C10 — C22×D5 — C2×C4×D5 — D10.12D4 — C10.742- 1+4
 Lower central C5 — C2×C10 — C10.742- 1+4
 Upper central C1 — C22 — C4⋊D4

Generators and relations for C10.742- 1+4
G = < a,b,c,d,e | a10=b4=c2=1, d2=e2=b2, bab-1=dad-1=a-1, ac=ca, ae=ea, cbc=b-1, bd=db, ebe-1=a5b, dcd-1=a5c, ce=ec, ede-1=a5b2d >

Subgroups: 790 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×D4, C2×Q8, Dic5, C20, D10, C2×C10, C2×C10, C4⋊D4, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42.C2, Dic10, C4×D5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C5×D4, 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, C22×Dic5, C2×C5⋊D4, C22×C20, D4×C10, Dic5.14D4, D10.12D4, Dic5.5D4, Dic5.Q8, D10⋊Q8, C20.48D4, C23.23D10, C23.18D10, C20.17D4, C202D4, Dic5⋊D4, C5×C4⋊D4, C10.742- 1+4
Quotients: C1, C2, C22, C23, D5, C24, D10, 2+ 1+4, 2- 1+4, C22×D5, C22.56C24, C23×D5, D46D10, D4.10D10, C10.742- 1+4

Smallest permutation representation of C10.742- 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 50 25 33)(2 49 26 32)(3 48 27 31)(4 47 28 40)(5 46 29 39)(6 45 30 38)(7 44 21 37)(8 43 22 36)(9 42 23 35)(10 41 24 34)(11 138 158 145)(12 137 159 144)(13 136 160 143)(14 135 151 142)(15 134 152 141)(16 133 153 150)(17 132 154 149)(18 131 155 148)(19 140 156 147)(20 139 157 146)(51 87 68 80)(52 86 69 79)(53 85 70 78)(54 84 61 77)(55 83 62 76)(56 82 63 75)(57 81 64 74)(58 90 65 73)(59 89 66 72)(60 88 67 71)(91 115 108 122)(92 114 109 121)(93 113 110 130)(94 112 101 129)(95 111 102 128)(96 120 103 127)(97 119 104 126)(98 118 105 125)(99 117 106 124)(100 116 107 123)
(1 38)(2 39)(3 40)(4 31)(5 32)(6 33)(7 34)(8 35)(9 36)(10 37)(11 145)(12 146)(13 147)(14 148)(15 149)(16 150)(17 141)(18 142)(19 143)(20 144)(21 41)(22 42)(23 43)(24 44)(25 45)(26 46)(27 47)(28 48)(29 49)(30 50)(51 83)(52 84)(53 85)(54 86)(55 87)(56 88)(57 89)(58 90)(59 81)(60 82)(61 79)(62 80)(63 71)(64 72)(65 73)(66 74)(67 75)(68 76)(69 77)(70 78)(91 123)(92 124)(93 125)(94 126)(95 127)(96 128)(97 129)(98 130)(99 121)(100 122)(101 119)(102 120)(103 111)(104 112)(105 113)(106 114)(107 115)(108 116)(109 117)(110 118)(131 151)(132 152)(133 153)(134 154)(135 155)(136 156)(137 157)(138 158)(139 159)(140 160)
(1 90 25 73)(2 89 26 72)(3 88 27 71)(4 87 28 80)(5 86 29 79)(6 85 30 78)(7 84 21 77)(8 83 22 76)(9 82 23 75)(10 81 24 74)(11 93 158 110)(12 92 159 109)(13 91 160 108)(14 100 151 107)(15 99 152 106)(16 98 153 105)(17 97 154 104)(18 96 155 103)(19 95 156 102)(20 94 157 101)(31 60 48 67)(32 59 49 66)(33 58 50 65)(34 57 41 64)(35 56 42 63)(36 55 43 62)(37 54 44 61)(38 53 45 70)(39 52 46 69)(40 51 47 68)(111 147 128 140)(112 146 129 139)(113 145 130 138)(114 144 121 137)(115 143 122 136)(116 142 123 135)(117 141 124 134)(118 150 125 133)(119 149 126 132)(120 148 127 131)
(1 11 25 158)(2 12 26 159)(3 13 27 160)(4 14 28 151)(5 15 29 152)(6 16 30 153)(7 17 21 154)(8 18 22 155)(9 19 23 156)(10 20 24 157)(31 148 48 131)(32 149 49 132)(33 150 50 133)(34 141 41 134)(35 142 42 135)(36 143 43 136)(37 144 44 137)(38 145 45 138)(39 146 46 139)(40 147 47 140)(51 116 68 123)(52 117 69 124)(53 118 70 125)(54 119 61 126)(55 120 62 127)(56 111 63 128)(57 112 64 129)(58 113 65 130)(59 114 66 121)(60 115 67 122)(71 96 88 103)(72 97 89 104)(73 98 90 105)(74 99 81 106)(75 100 82 107)(76 91 83 108)(77 92 84 109)(78 93 85 110)(79 94 86 101)(80 95 87 102)```

`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), (1,50,25,33)(2,49,26,32)(3,48,27,31)(4,47,28,40)(5,46,29,39)(6,45,30,38)(7,44,21,37)(8,43,22,36)(9,42,23,35)(10,41,24,34)(11,138,158,145)(12,137,159,144)(13,136,160,143)(14,135,151,142)(15,134,152,141)(16,133,153,150)(17,132,154,149)(18,131,155,148)(19,140,156,147)(20,139,157,146)(51,87,68,80)(52,86,69,79)(53,85,70,78)(54,84,61,77)(55,83,62,76)(56,82,63,75)(57,81,64,74)(58,90,65,73)(59,89,66,72)(60,88,67,71)(91,115,108,122)(92,114,109,121)(93,113,110,130)(94,112,101,129)(95,111,102,128)(96,120,103,127)(97,119,104,126)(98,118,105,125)(99,117,106,124)(100,116,107,123), (1,38)(2,39)(3,40)(4,31)(5,32)(6,33)(7,34)(8,35)(9,36)(10,37)(11,145)(12,146)(13,147)(14,148)(15,149)(16,150)(17,141)(18,142)(19,143)(20,144)(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(51,83)(52,84)(53,85)(54,86)(55,87)(56,88)(57,89)(58,90)(59,81)(60,82)(61,79)(62,80)(63,71)(64,72)(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(91,123)(92,124)(93,125)(94,126)(95,127)(96,128)(97,129)(98,130)(99,121)(100,122)(101,119)(102,120)(103,111)(104,112)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(131,151)(132,152)(133,153)(134,154)(135,155)(136,156)(137,157)(138,158)(139,159)(140,160), (1,90,25,73)(2,89,26,72)(3,88,27,71)(4,87,28,80)(5,86,29,79)(6,85,30,78)(7,84,21,77)(8,83,22,76)(9,82,23,75)(10,81,24,74)(11,93,158,110)(12,92,159,109)(13,91,160,108)(14,100,151,107)(15,99,152,106)(16,98,153,105)(17,97,154,104)(18,96,155,103)(19,95,156,102)(20,94,157,101)(31,60,48,67)(32,59,49,66)(33,58,50,65)(34,57,41,64)(35,56,42,63)(36,55,43,62)(37,54,44,61)(38,53,45,70)(39,52,46,69)(40,51,47,68)(111,147,128,140)(112,146,129,139)(113,145,130,138)(114,144,121,137)(115,143,122,136)(116,142,123,135)(117,141,124,134)(118,150,125,133)(119,149,126,132)(120,148,127,131), (1,11,25,158)(2,12,26,159)(3,13,27,160)(4,14,28,151)(5,15,29,152)(6,16,30,153)(7,17,21,154)(8,18,22,155)(9,19,23,156)(10,20,24,157)(31,148,48,131)(32,149,49,132)(33,150,50,133)(34,141,41,134)(35,142,42,135)(36,143,43,136)(37,144,44,137)(38,145,45,138)(39,146,46,139)(40,147,47,140)(51,116,68,123)(52,117,69,124)(53,118,70,125)(54,119,61,126)(55,120,62,127)(56,111,63,128)(57,112,64,129)(58,113,65,130)(59,114,66,121)(60,115,67,122)(71,96,88,103)(72,97,89,104)(73,98,90,105)(74,99,81,106)(75,100,82,107)(76,91,83,108)(77,92,84,109)(78,93,85,110)(79,94,86,101)(80,95,87,102)>;`

`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), (1,50,25,33)(2,49,26,32)(3,48,27,31)(4,47,28,40)(5,46,29,39)(6,45,30,38)(7,44,21,37)(8,43,22,36)(9,42,23,35)(10,41,24,34)(11,138,158,145)(12,137,159,144)(13,136,160,143)(14,135,151,142)(15,134,152,141)(16,133,153,150)(17,132,154,149)(18,131,155,148)(19,140,156,147)(20,139,157,146)(51,87,68,80)(52,86,69,79)(53,85,70,78)(54,84,61,77)(55,83,62,76)(56,82,63,75)(57,81,64,74)(58,90,65,73)(59,89,66,72)(60,88,67,71)(91,115,108,122)(92,114,109,121)(93,113,110,130)(94,112,101,129)(95,111,102,128)(96,120,103,127)(97,119,104,126)(98,118,105,125)(99,117,106,124)(100,116,107,123), (1,38)(2,39)(3,40)(4,31)(5,32)(6,33)(7,34)(8,35)(9,36)(10,37)(11,145)(12,146)(13,147)(14,148)(15,149)(16,150)(17,141)(18,142)(19,143)(20,144)(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(51,83)(52,84)(53,85)(54,86)(55,87)(56,88)(57,89)(58,90)(59,81)(60,82)(61,79)(62,80)(63,71)(64,72)(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(91,123)(92,124)(93,125)(94,126)(95,127)(96,128)(97,129)(98,130)(99,121)(100,122)(101,119)(102,120)(103,111)(104,112)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(131,151)(132,152)(133,153)(134,154)(135,155)(136,156)(137,157)(138,158)(139,159)(140,160), (1,90,25,73)(2,89,26,72)(3,88,27,71)(4,87,28,80)(5,86,29,79)(6,85,30,78)(7,84,21,77)(8,83,22,76)(9,82,23,75)(10,81,24,74)(11,93,158,110)(12,92,159,109)(13,91,160,108)(14,100,151,107)(15,99,152,106)(16,98,153,105)(17,97,154,104)(18,96,155,103)(19,95,156,102)(20,94,157,101)(31,60,48,67)(32,59,49,66)(33,58,50,65)(34,57,41,64)(35,56,42,63)(36,55,43,62)(37,54,44,61)(38,53,45,70)(39,52,46,69)(40,51,47,68)(111,147,128,140)(112,146,129,139)(113,145,130,138)(114,144,121,137)(115,143,122,136)(116,142,123,135)(117,141,124,134)(118,150,125,133)(119,149,126,132)(120,148,127,131), (1,11,25,158)(2,12,26,159)(3,13,27,160)(4,14,28,151)(5,15,29,152)(6,16,30,153)(7,17,21,154)(8,18,22,155)(9,19,23,156)(10,20,24,157)(31,148,48,131)(32,149,49,132)(33,150,50,133)(34,141,41,134)(35,142,42,135)(36,143,43,136)(37,144,44,137)(38,145,45,138)(39,146,46,139)(40,147,47,140)(51,116,68,123)(52,117,69,124)(53,118,70,125)(54,119,61,126)(55,120,62,127)(56,111,63,128)(57,112,64,129)(58,113,65,130)(59,114,66,121)(60,115,67,122)(71,96,88,103)(72,97,89,104)(73,98,90,105)(74,99,81,106)(75,100,82,107)(76,91,83,108)(77,92,84,109)(78,93,85,110)(79,94,86,101)(80,95,87,102) );`

`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)], [(1,50,25,33),(2,49,26,32),(3,48,27,31),(4,47,28,40),(5,46,29,39),(6,45,30,38),(7,44,21,37),(8,43,22,36),(9,42,23,35),(10,41,24,34),(11,138,158,145),(12,137,159,144),(13,136,160,143),(14,135,151,142),(15,134,152,141),(16,133,153,150),(17,132,154,149),(18,131,155,148),(19,140,156,147),(20,139,157,146),(51,87,68,80),(52,86,69,79),(53,85,70,78),(54,84,61,77),(55,83,62,76),(56,82,63,75),(57,81,64,74),(58,90,65,73),(59,89,66,72),(60,88,67,71),(91,115,108,122),(92,114,109,121),(93,113,110,130),(94,112,101,129),(95,111,102,128),(96,120,103,127),(97,119,104,126),(98,118,105,125),(99,117,106,124),(100,116,107,123)], [(1,38),(2,39),(3,40),(4,31),(5,32),(6,33),(7,34),(8,35),(9,36),(10,37),(11,145),(12,146),(13,147),(14,148),(15,149),(16,150),(17,141),(18,142),(19,143),(20,144),(21,41),(22,42),(23,43),(24,44),(25,45),(26,46),(27,47),(28,48),(29,49),(30,50),(51,83),(52,84),(53,85),(54,86),(55,87),(56,88),(57,89),(58,90),(59,81),(60,82),(61,79),(62,80),(63,71),(64,72),(65,73),(66,74),(67,75),(68,76),(69,77),(70,78),(91,123),(92,124),(93,125),(94,126),(95,127),(96,128),(97,129),(98,130),(99,121),(100,122),(101,119),(102,120),(103,111),(104,112),(105,113),(106,114),(107,115),(108,116),(109,117),(110,118),(131,151),(132,152),(133,153),(134,154),(135,155),(136,156),(137,157),(138,158),(139,159),(140,160)], [(1,90,25,73),(2,89,26,72),(3,88,27,71),(4,87,28,80),(5,86,29,79),(6,85,30,78),(7,84,21,77),(8,83,22,76),(9,82,23,75),(10,81,24,74),(11,93,158,110),(12,92,159,109),(13,91,160,108),(14,100,151,107),(15,99,152,106),(16,98,153,105),(17,97,154,104),(18,96,155,103),(19,95,156,102),(20,94,157,101),(31,60,48,67),(32,59,49,66),(33,58,50,65),(34,57,41,64),(35,56,42,63),(36,55,43,62),(37,54,44,61),(38,53,45,70),(39,52,46,69),(40,51,47,68),(111,147,128,140),(112,146,129,139),(113,145,130,138),(114,144,121,137),(115,143,122,136),(116,142,123,135),(117,141,124,134),(118,150,125,133),(119,149,126,132),(120,148,127,131)], [(1,11,25,158),(2,12,26,159),(3,13,27,160),(4,14,28,151),(5,15,29,152),(6,16,30,153),(7,17,21,154),(8,18,22,155),(9,19,23,156),(10,20,24,157),(31,148,48,131),(32,149,49,132),(33,150,50,133),(34,141,41,134),(35,142,42,135),(36,143,43,136),(37,144,44,137),(38,145,45,138),(39,146,46,139),(40,147,47,140),(51,116,68,123),(52,117,69,124),(53,118,70,125),(54,119,61,126),(55,120,62,127),(56,111,63,128),(57,112,64,129),(58,113,65,130),(59,114,66,121),(60,115,67,122),(71,96,88,103),(72,97,89,104),(73,98,90,105),(74,99,81,106),(75,100,82,107),(76,91,83,108),(77,92,84,109),(78,93,85,110),(79,94,86,101),(80,95,87,102)]])`

47 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 4A 4B 4C 4D 4E ··· 4K 5A 5B 10A ··· 10F 10G 10H 10I 10J 10K 10L 10M 10N 20A ··· 20H 20I 20J 20K 20L order 1 2 2 2 2 2 2 2 4 4 4 4 4 ··· 4 5 5 10 ··· 10 10 10 10 10 10 10 10 10 20 ··· 20 20 20 20 20 size 1 1 1 1 4 4 4 20 4 4 4 4 20 ··· 20 2 2 2 ··· 2 4 4 4 4 8 8 8 8 4 ··· 4 8 8 8 8

47 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 4 4 4 4 type + + + + + + + + + + + + + + + + + + + - - image C1 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 D4.10D10 kernel C10.742- 1+4 Dic5.14D4 D10.12D4 Dic5.5D4 Dic5.Q8 D10⋊Q8 C20.48D4 C23.23D10 C23.18D10 C20.17D4 C20⋊2D4 Dic5⋊D4 C5×C4⋊D4 C4⋊D4 C22⋊C4 C4⋊C4 C22×C4 C2×D4 C10 C10 C2 C2 # reps 1 2 1 1 1 1 1 1 2 1 1 2 1 2 4 2 2 6 2 1 8 4

Matrix representation of C10.742- 1+4 in GL8(𝔽41)

 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 34 7 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 34 7
,
 0 40 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 7 40 0 0 0 0 0 0 7 34 0 0 0 0 7 40 0 0 0 0 0 0 7 34 0 0
,
 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
,
 0 0 0 40 0 0 0 0 0 0 1 0 0 0 0 0 0 40 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 22 9 40 35 0 0 0 0 2 19 26 1 0 0 0 0 1 6 19 32 0 0 0 0 15 40 39 22
,
 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 0 0 0 17 6 0 0 0 0 0 0 34 24 0 0 0 0 0 0 0 0 17 6 0 0 0 0 0 0 34 24

`G:=sub<GL(8,GF(41))| [40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,34,0,0,0,0,0,0,6,7,0,0,0,0,0,0,0,0,0,34,0,0,0,0,0,0,6,7],[0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,0,7,7,0,0,0,0,0,0,40,34,0,0,0,0,7,7,0,0,0,0,0,0,40,34,0,0],[0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,0,22,2,1,15,0,0,0,0,9,19,6,40,0,0,0,0,40,26,19,39,0,0,0,0,35,1,32,22],[0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,17,34,0,0,0,0,0,0,6,24,0,0,0,0,0,0,0,0,17,34,0,0,0,0,0,0,6,24] >;`

C10.742- 1+4 in GAP, Magma, Sage, TeX

`C_{10}._{74}2_-^{1+4}`
`% in TeX`

`G:=Group("C10.74ES-(2,2)");`
`// GroupNames label`

`G:=SmallGroup(320,1293);`
`// by ID`

`G=gap.SmallGroup(320,1293);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,758,219,1571,570,297,12550]);`
`// Polycyclic`

`G:=Group<a,b,c,d,e|a^10=b^4=c^2=1,d^2=e^2=b^2,b*a*b^-1=d*a*d^-1=a^-1,a*c=c*a,a*e=e*a,c*b*c=b^-1,b*d=d*b,e*b*e^-1=a^5*b,d*c*d^-1=a^5*c,c*e=e*c,e*d*e^-1=a^5*b^2*d>;`
`// generators/relations`

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