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## G = C10.392+ 1+4order 320 = 26·5

### 39th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C10 — C10.392+ 1+4
 Chief series C1 — C5 — C10 — C2×C10 — C22×D5 — C2×C4×D5 — C2×C4○D20 — C10.392+ 1+4
 Lower central C5 — C2×C10 — C10.392+ 1+4
 Upper central C1 — C22 — C4⋊D4

Generators and relations for C10.392+ 1+4
G = < a,b,c,d,e | a10=b4=e2=1, c2=a5, d2=b2, bab-1=cac-1=a-1, ad=da, ae=ea, cbc-1=a5b-1, dbd-1=a5b, be=eb, dcd-1=ece=a5c, ede=a5b2d >

Subgroups: 1102 in 294 conjugacy classes, 103 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C5, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, C23, D5, C10, C10, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic5, Dic5, C20, C20, D10, D10, C2×C10, C2×C10, C2×C4⋊C4, C4⋊D4, C4⋊D4, C22⋊Q8, C2×C4○D4, Dic10, C4×D5, C4×D5, D20, C2×Dic5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C2×C20, C5×D4, C22×D5, C22×C10, C22×C10, C22.31C24, C10.D4, C4⋊Dic5, C4⋊Dic5, D10⋊C4, C23.D5, C5×C22⋊C4, C5×C4⋊C4, C2×Dic10, C2×C4×D5, C2×C4×D5, C2×D20, C4○D20, D42D5, C22×Dic5, C2×C5⋊D4, C2×C5⋊D4, C22×C20, D4×C10, D4×C10, Dic5.14D4, D10⋊D4, D5×C4⋊C4, D102Q8, C20.48D4, C202D4, C202D4, Dic5⋊D4, C5×C4⋊D4, C2×C4○D20, C2×D42D5, C10.392+ 1+4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C24, D10, C22×D4, 2+ 1+4, 2- 1+4, C22×D5, C22.31C24, D4×D5, C23×D5, C2×D4×D5, D46D10, D4.10D10, C10.392+ 1+4

Smallest permutation representation of C10.392+ 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 90 30 72)(2 89 21 71)(3 88 22 80)(4 87 23 79)(5 86 24 78)(6 85 25 77)(7 84 26 76)(8 83 27 75)(9 82 28 74)(10 81 29 73)(11 97 157 105)(12 96 158 104)(13 95 159 103)(14 94 160 102)(15 93 151 101)(16 92 152 110)(17 91 153 109)(18 100 154 108)(19 99 155 107)(20 98 156 106)(31 66 49 58)(32 65 50 57)(33 64 41 56)(34 63 42 55)(35 62 43 54)(36 61 44 53)(37 70 45 52)(38 69 46 51)(39 68 47 60)(40 67 48 59)(111 138 129 146)(112 137 130 145)(113 136 121 144)(114 135 122 143)(115 134 123 142)(116 133 124 141)(117 132 125 150)(118 131 126 149)(119 140 127 148)(120 139 128 147)
(1 45 6 50)(2 44 7 49)(3 43 8 48)(4 42 9 47)(5 41 10 46)(11 132 16 137)(12 131 17 136)(13 140 18 135)(14 139 19 134)(15 138 20 133)(21 36 26 31)(22 35 27 40)(23 34 28 39)(24 33 29 38)(25 32 30 37)(51 73 56 78)(52 72 57 77)(53 71 58 76)(54 80 59 75)(55 79 60 74)(61 89 66 84)(62 88 67 83)(63 87 68 82)(64 86 69 81)(65 85 70 90)(91 118 96 113)(92 117 97 112)(93 116 98 111)(94 115 99 120)(95 114 100 119)(101 124 106 129)(102 123 107 128)(103 122 108 127)(104 121 109 126)(105 130 110 125)(141 151 146 156)(142 160 147 155)(143 159 148 154)(144 158 149 153)(145 157 150 152)
(1 150 30 132)(2 141 21 133)(3 142 22 134)(4 143 23 135)(5 144 24 136)(6 145 25 137)(7 146 26 138)(8 147 27 139)(9 148 28 140)(10 149 29 131)(11 45 157 37)(12 46 158 38)(13 47 159 39)(14 48 160 40)(15 49 151 31)(16 50 152 32)(17 41 153 33)(18 42 154 34)(19 43 155 35)(20 44 156 36)(51 109 69 91)(52 110 70 92)(53 101 61 93)(54 102 62 94)(55 103 63 95)(56 104 64 96)(57 105 65 97)(58 106 66 98)(59 107 67 99)(60 108 68 100)(71 129 89 111)(72 130 90 112)(73 121 81 113)(74 122 82 114)(75 123 83 115)(76 124 84 116)(77 125 85 117)(78 126 86 118)(79 127 87 119)(80 128 88 120)
(1 37)(2 38)(3 39)(4 40)(5 31)(6 32)(7 33)(8 34)(9 35)(10 36)(11 137)(12 138)(13 139)(14 140)(15 131)(16 132)(17 133)(18 134)(19 135)(20 136)(21 46)(22 47)(23 48)(24 49)(25 50)(26 41)(27 42)(28 43)(29 44)(30 45)(51 71)(52 72)(53 73)(54 74)(55 75)(56 76)(57 77)(58 78)(59 79)(60 80)(61 81)(62 82)(63 83)(64 84)(65 85)(66 86)(67 87)(68 88)(69 89)(70 90)(91 124)(92 125)(93 126)(94 127)(95 128)(96 129)(97 130)(98 121)(99 122)(100 123)(101 118)(102 119)(103 120)(104 111)(105 112)(106 113)(107 114)(108 115)(109 116)(110 117)(141 153)(142 154)(143 155)(144 156)(145 157)(146 158)(147 159)(148 160)(149 151)(150 152)```

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

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

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

50 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 2H 2I 4A 4B 4C 4D 4E 4F 4G 4H ··· 4L 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 2 2 4 4 4 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 10 10 20 2 2 4 4 4 10 10 20 ··· 20 2 2 2 ··· 2 4 4 4 4 8 8 8 8 4 ··· 4 8 8 8 8

50 irreducible representations

 dim 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 D4 D5 D10 D10 D10 D10 2+ 1+4 2- 1+4 D4×D5 D4⋊6D10 D4.10D10 kernel C10.392+ 1+4 Dic5.14D4 D10⋊D4 D5×C4⋊C4 D10⋊2Q8 C20.48D4 C20⋊2D4 Dic5⋊D4 C5×C4⋊D4 C2×C4○D20 C2×D4⋊2D5 C4×D5 C4⋊D4 C22⋊C4 C4⋊C4 C22×C4 C2×D4 C10 C10 C4 C2 C2 # reps 1 2 2 1 1 1 3 2 1 1 1 4 2 4 2 2 6 1 1 4 4 4

Matrix representation of C10.392+ 1+4 in GL8(𝔽41)

 7 7 0 0 0 0 0 0 34 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 40 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 40
,
 40 0 0 0 0 0 0 0 7 1 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 1 0 0 39 0 0 0 0 40 0 40 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 40
,
 1 0 0 0 0 0 0 0 34 40 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 1 2 0 0 0 0 0 0 40 40 0 0 0 0 0 0 0 40 0 40 0 0 0 0 1 1 1 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 1 0 0 0 0 0 0 0 0 18 35 1 0 0 0 0 0 20 3 20 21 0 0 0 0 0 3 20 3 0 0 0 0 21 18 24 0
,
 1 0 0 0 0 0 0 0 0 1 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 1 2 0 0 0 0 0 0 0 40 0 0 0 0 0 0 40 40 0 1 0 0 0 0 1 1 1 0

`G:=sub<GL(8,GF(41))| [7,34,0,0,0,0,0,0,7,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40],[40,7,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,40,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,39,1,1,40],[1,34,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,1,40,0,1,0,0,0,0,2,40,40,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0],[40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,18,20,0,21,0,0,0,0,35,3,3,18,0,0,0,0,1,20,20,24,0,0,0,0,0,21,3,0],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,40,1,0,0,0,0,2,40,40,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;`

C10.392+ 1+4 in GAP, Magma, Sage, TeX

`C_{10}._{39}2_+^{1+4}`
`% in TeX`

`G:=Group("C10.39ES+(2,2)");`
`// GroupNames label`

`G:=SmallGroup(320,1280);`
`// by ID`

`G=gap.SmallGroup(320,1280);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,758,1123,570,185,12550]);`
`// Polycyclic`

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

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