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G = C10.842- 1+4order 320 = 26·5

39th non-split extension by C10 of 2- 1+4 acting via 2- 1+4/C4○D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.842- 1+4, C10.652+ 1+4, C20⋊Q833C2, C4⋊C4.199D10, D10⋊Q832C2, (C2×D4).102D10, C22⋊C4.29D10, Dic53Q832C2, C20.48D423C2, C20.17D422C2, (C2×C10).206C24, (C2×C20).181C23, Dic5⋊D4.2C2, C22.D411D5, (C22×C4).260D10, C4⋊Dic5.49C22, D10.12D435C2, C2.67(D46D10), C23.30(C22×D5), Dic5.15(C4○D4), Dic5.5D434C2, (D4×C10).144C22, C23.D1034C2, (C22×C10).38C23, (C22×D5).87C23, C22.227(C23×D5), Dic5.14D434C2, C23.D5.45C22, D10⋊C4.34C22, C23.11D1015C2, (C22×C20).116C22, C57(C22.36C24), (C4×Dic5).133C22, (C2×Dic5).107C23, C10.D4.44C22, C2.45(D4.10D10), (C2×Dic10).175C22, (C22×Dic5).132C22, (C4×C5⋊D4)⋊8C2, C2.68(D5×C4○D4), C4⋊C4⋊D530C2, C10.180(C2×C4○D4), (C2×C4×D5).263C22, (C2×C4).68(C22×D5), (C5×C4⋊C4).179C22, (C2×C5⋊D4).50C22, (C5×C22.D4)⋊14C2, (C5×C22⋊C4).54C22, SmallGroup(320,1334)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C10.842- 1+4
C1C5C10C2×C10C22×D5C2×C4×D5D10.12D4 — C10.842- 1+4
C5C2×C10 — C10.842- 1+4
C1C22C22.D4

Generators and relations for C10.842- 1+4
 G = < a,b,c,d,e | a10=b4=c2=1, d2=b2, e2=a5b2, bab-1=dad-1=a-1, ac=ca, ae=ea, cbc=b-1, bd=db, be=eb, dcd-1=a5c, ce=ec, ede-1=b2d >

Subgroups: 734 in 216 conjugacy classes, 93 normal (91 characteristic)
C1, C2 [×3], C2 [×3], C4 [×13], C22, C22 [×9], C5, C2×C4 [×5], C2×C4 [×11], D4 [×4], Q8 [×4], C23 [×2], C23, D5, C10 [×3], C10 [×2], C42 [×4], C22⋊C4 [×3], C22⋊C4 [×9], C4⋊C4 [×2], C4⋊C4 [×8], C22×C4, C22×C4 [×2], C2×D4, C2×D4 [×2], C2×Q8 [×3], Dic5 [×2], Dic5 [×6], C20 [×5], D10 [×3], C2×C10, C2×C10 [×6], C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8 [×3], C22.D4, C22.D4, C4.4D4 [×3], C422C2 [×2], C4⋊Q8, Dic10 [×4], C4×D5, C2×Dic5 [×7], C2×Dic5 [×2], C5⋊D4 [×3], C2×C20 [×5], C2×C20, C5×D4, C22×D5, C22×C10 [×2], C22.36C24, C4×Dic5 [×4], C10.D4 [×6], C4⋊Dic5 [×2], D10⋊C4 [×4], C23.D5 [×5], C5×C22⋊C4 [×3], C5×C4⋊C4 [×2], C2×Dic10 [×3], C2×C4×D5, C22×Dic5, C2×C5⋊D4 [×2], C22×C20, D4×C10, C23.11D10, Dic5.14D4, C23.D10, D10.12D4, Dic5.5D4 [×2], Dic53Q8, C20⋊Q8, D10⋊Q8, C4⋊C4⋊D5, C20.48D4, C4×C5⋊D4, C20.17D4, Dic5⋊D4, C5×C22.D4, C10.842- 1+4
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], D5, C4○D4 [×2], C24, D10 [×7], C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D5 [×7], C22.36C24, C23×D5, D46D10, D5×C4○D4, D4.10D10, C10.842- 1+4

Smallest permutation representation of C10.842- 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 38 22 50)(2 37 23 49)(3 36 24 48)(4 35 25 47)(5 34 26 46)(6 33 27 45)(7 32 28 44)(8 31 29 43)(9 40 30 42)(10 39 21 41)(11 150 153 138)(12 149 154 137)(13 148 155 136)(14 147 156 135)(15 146 157 134)(16 145 158 133)(17 144 159 132)(18 143 160 131)(19 142 151 140)(20 141 152 139)(51 82 63 80)(52 81 64 79)(53 90 65 78)(54 89 66 77)(55 88 67 76)(56 87 68 75)(57 86 69 74)(58 85 70 73)(59 84 61 72)(60 83 62 71)(91 122 103 120)(92 121 104 119)(93 130 105 118)(94 129 106 117)(95 128 107 116)(96 127 108 115)(97 126 109 114)(98 125 110 113)(99 124 101 112)(100 123 102 111)
(1 45)(2 46)(3 47)(4 48)(5 49)(6 50)(7 41)(8 42)(9 43)(10 44)(11 138)(12 139)(13 140)(14 131)(15 132)(16 133)(17 134)(18 135)(19 136)(20 137)(21 32)(22 33)(23 34)(24 35)(25 36)(26 37)(27 38)(28 39)(29 40)(30 31)(51 88)(52 89)(53 90)(54 81)(55 82)(56 83)(57 84)(58 85)(59 86)(60 87)(61 74)(62 75)(63 76)(64 77)(65 78)(66 79)(67 80)(68 71)(69 72)(70 73)(91 111)(92 112)(93 113)(94 114)(95 115)(96 116)(97 117)(98 118)(99 119)(100 120)(101 121)(102 122)(103 123)(104 124)(105 125)(106 126)(107 127)(108 128)(109 129)(110 130)(141 154)(142 155)(143 156)(144 157)(145 158)(146 159)(147 160)(148 151)(149 152)(150 153)
(1 85 22 73)(2 84 23 72)(3 83 24 71)(4 82 25 80)(5 81 26 79)(6 90 27 78)(7 89 28 77)(8 88 29 76)(9 87 30 75)(10 86 21 74)(11 105 153 93)(12 104 154 92)(13 103 155 91)(14 102 156 100)(15 101 157 99)(16 110 158 98)(17 109 159 97)(18 108 160 96)(19 107 151 95)(20 106 152 94)(31 67 43 55)(32 66 44 54)(33 65 45 53)(34 64 46 52)(35 63 47 51)(36 62 48 60)(37 61 49 59)(38 70 50 58)(39 69 41 57)(40 68 42 56)(111 135 123 147)(112 134 124 146)(113 133 125 145)(114 132 126 144)(115 131 127 143)(116 140 128 142)(117 139 129 141)(118 138 130 150)(119 137 121 149)(120 136 122 148)
(1 98 27 105)(2 99 28 106)(3 100 29 107)(4 91 30 108)(5 92 21 109)(6 93 22 110)(7 94 23 101)(8 95 24 102)(9 96 25 103)(10 97 26 104)(11 85 158 78)(12 86 159 79)(13 87 160 80)(14 88 151 71)(15 89 152 72)(16 90 153 73)(17 81 154 74)(18 82 155 75)(19 83 156 76)(20 84 157 77)(31 128 48 111)(32 129 49 112)(33 130 50 113)(34 121 41 114)(35 122 42 115)(36 123 43 116)(37 124 44 117)(38 125 45 118)(39 126 46 119)(40 127 47 120)(51 148 68 131)(52 149 69 132)(53 150 70 133)(54 141 61 134)(55 142 62 135)(56 143 63 136)(57 144 64 137)(58 145 65 138)(59 146 66 139)(60 147 67 140)

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

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

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

50 conjugacy classes

class 1 2A2B2C2D2E2F4A4B4C4D4E4F4G4H4I4J4K···4O5A5B10A···10F10G10H10I10J10K10L20A···20H20I···20N
order122222244444444444···45510···1010101010101020···2020···20
size111144202244441010101020···20222···24444884···48···8

50 irreducible representations

dim11111111111111122222244444
type+++++++++++++++++++++--
imageC1C2C2C2C2C2C2C2C2C2C2C2C2C2C2D5C4○D4D10D10D10D102+ 1+42- 1+4D46D10D5×C4○D4D4.10D10
kernelC10.842- 1+4C23.11D10Dic5.14D4C23.D10D10.12D4Dic5.5D4Dic53Q8C20⋊Q8D10⋊Q8C4⋊C4⋊D5C20.48D4C4×C5⋊D4C20.17D4Dic5⋊D4C5×C22.D4C22.D4Dic5C22⋊C4C4⋊C4C22×C4C2×D4C10C10C2C2C2
# reps11111211111111124642211444

Matrix representation of C10.842- 1+4 in GL8(𝔽41)

06000000
347000000
00060000
003470000
000003500
000073400
000000035
000000734
,
007400000
007340000
740000000
734000000
00003181439
00004381427
000000318
000000438
,
00100000
00010000
10000000
01000000
000017620
0000342402
0000002435
000000717
,
37175300000
22434360000
36114240000
7519370000
000032132739
00003293614
00002123213
00003039329
,
320000000
032000000
003200000
000320000
00003202215
0000032319
00000090
00000009

G:=sub<GL(8,GF(41))| [0,34,0,0,0,0,0,0,6,7,0,0,0,0,0,0,0,0,0,34,0,0,0,0,0,0,6,7,0,0,0,0,0,0,0,0,0,7,0,0,0,0,0,0,35,34,0,0,0,0,0,0,0,0,0,7,0,0,0,0,0,0,35,34],[0,0,7,7,0,0,0,0,0,0,40,34,0,0,0,0,7,7,0,0,0,0,0,0,40,34,0,0,0,0,0,0,0,0,0,0,3,4,0,0,0,0,0,0,18,38,0,0,0,0,0,0,14,14,3,4,0,0,0,0,39,27,18,38],[0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,17,34,0,0,0,0,0,0,6,24,0,0,0,0,0,0,2,0,24,7,0,0,0,0,0,2,35,17],[37,22,36,7,0,0,0,0,17,4,11,5,0,0,0,0,5,34,4,19,0,0,0,0,30,36,24,37,0,0,0,0,0,0,0,0,32,32,2,30,0,0,0,0,13,9,12,39,0,0,0,0,27,36,32,32,0,0,0,0,39,14,13,9],[32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,22,3,9,0,0,0,0,0,15,19,0,9] >;

C10.842- 1+4 in GAP, Magma, Sage, TeX

C_{10}._{84}2_-^{1+4}
% in TeX

G:=Group("C10.84ES-(2,2)");
// GroupNames label

G:=SmallGroup(320,1334);
// by ID

G=gap.SmallGroup(320,1334);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,758,219,675,297,12550]);
// 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,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,b*e=e*b,d*c*d^-1=a^5*c,c*e=e*c,e*d*e^-1=b^2*d>;
// generators/relations

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