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G = C10.632+ 1+4order 320 = 26·5

63rd non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.632+ 1+4, C10.832- 1+4, C4⋊C4.107D10, D10⋊Q831C2, (C2×D4).100D10, C202D4.12C2, C22⋊C4.28D10, C4.Dic1029C2, C22.D49D5, D10.13(C4○D4), Dic54D422C2, C20.48D422C2, (C2×C20).180C23, (C2×C10).204C24, (C22×C4).259D10, D10.12D433C2, C2.65(D46D10), C23.28(C22×D5), Dic5.Q827C2, (D4×C10).142C22, C23.D1032C2, C4⋊Dic5.228C22, (C22×C10).36C23, C22.225(C23×D5), Dic5.14D433C2, C23.D5.44C22, C23.18D1015C2, (C22×C20).115C22, C56(C22.33C24), (C2×Dic5).106C23, (C4×Dic5).132C22, (C2×Dic10).39C22, C10.D4.42C22, (C22×D5).220C23, C2.44(D4.10D10), D10⋊C4.108C22, (C22×Dic5).130C22, (D5×C4⋊C4)⋊33C2, (C4×C5⋊D4)⋊7C2, C2.66(D5×C4○D4), C10.178(C2×C4○D4), (C2×C4×D5).122C22, (C2×C4).66(C22×D5), (C5×C4⋊C4).177C22, (C2×C5⋊D4).48C22, (C5×C22.D4)⋊12C2, (C5×C22⋊C4).52C22, SmallGroup(320,1332)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C10.632+ 1+4
C1C5C10C2×C10C22×D5C2×C4×D5D5×C4⋊C4 — C10.632+ 1+4
C5C2×C10 — C10.632+ 1+4
C1C22C22.D4

Generators and relations for C10.632+ 1+4
 G = < a,b,c,d,e | a10=b4=e2=1, c2=a5, d2=b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc-1=b-1, dbd-1=ebe=a5b, cd=dc, ce=ec, ede=b2d >

Subgroups: 734 in 218 conjugacy classes, 93 normal (91 characteristic)
C1, C2 [×3], C2 [×4], C4 [×12], C22, C22 [×10], C5, C2×C4 [×5], C2×C4 [×13], D4 [×5], Q8, C23 [×2], C23, D5 [×2], C10 [×3], C10 [×2], C42 [×2], C22⋊C4 [×3], C22⋊C4 [×7], C4⋊C4 [×2], C4⋊C4 [×12], C22×C4, C22×C4 [×4], C2×D4, C2×D4 [×2], C2×Q8, Dic5 [×7], C20 [×5], D10 [×2], D10 [×2], C2×C10, C2×C10 [×6], C2×C4⋊C4, C4×D4 [×2], C4⋊D4, C22⋊Q8 [×3], C22.D4, C22.D4 [×3], C42.C2 [×2], C422C2 [×2], Dic10, C4×D5 [×4], C2×Dic5 [×7], C2×Dic5, C5⋊D4 [×4], C2×C20 [×5], C2×C20, C5×D4, C22×D5, C22×C10 [×2], C22.33C24, C4×Dic5 [×2], C10.D4 [×8], C4⋊Dic5 [×4], D10⋊C4 [×2], C23.D5 [×5], C5×C22⋊C4 [×3], C5×C4⋊C4 [×2], C2×Dic10, C2×C4×D5 [×3], C22×Dic5, C2×C5⋊D4 [×2], C22×C20, D4×C10, Dic5.14D4, C23.D10 [×2], Dic54D4, D10.12D4 [×2], Dic5.Q8, C4.Dic10, D5×C4⋊C4, D10⋊Q8, C20.48D4, C4×C5⋊D4, C23.18D10, C202D4, C5×C22.D4, C10.632+ 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], C22.33C24, C23×D5, D46D10, D5×C4○D4, D4.10D10, C10.632+ 1+4

Smallest permutation representation of C10.632+ 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)
(1 133 13 123)(2 134 14 124)(3 135 15 125)(4 136 16 126)(5 137 17 127)(6 138 18 128)(7 139 19 129)(8 140 20 130)(9 131 11 121)(10 132 12 122)(21 151 31 141)(22 152 32 142)(23 153 33 143)(24 154 34 144)(25 155 35 145)(26 156 36 146)(27 157 37 147)(28 158 38 148)(29 159 39 149)(30 160 40 150)(41 96 51 86)(42 97 52 87)(43 98 53 88)(44 99 54 89)(45 100 55 90)(46 91 56 81)(47 92 57 82)(48 93 58 83)(49 94 59 84)(50 95 60 85)(61 116 71 106)(62 117 72 107)(63 118 73 108)(64 119 74 109)(65 120 75 110)(66 111 76 101)(67 112 77 102)(68 113 78 103)(69 114 79 104)(70 115 80 105)
(1 88 6 83)(2 89 7 84)(3 90 8 85)(4 81 9 86)(5 82 10 87)(11 96 16 91)(12 97 17 92)(13 98 18 93)(14 99 19 94)(15 100 20 95)(21 106 26 101)(22 107 27 102)(23 108 28 103)(24 109 29 104)(25 110 30 105)(31 116 36 111)(32 117 37 112)(33 118 38 113)(34 119 39 114)(35 120 40 115)(41 126 46 121)(42 127 47 122)(43 128 48 123)(44 129 49 124)(45 130 50 125)(51 136 56 131)(52 137 57 132)(53 138 58 133)(54 139 59 134)(55 140 60 135)(61 146 66 141)(62 147 67 142)(63 148 68 143)(64 149 69 144)(65 150 70 145)(71 156 76 151)(72 157 77 152)(73 158 78 153)(74 159 79 154)(75 160 80 155)
(1 33 13 23)(2 32 14 22)(3 31 15 21)(4 40 16 30)(5 39 17 29)(6 38 18 28)(7 37 19 27)(8 36 20 26)(9 35 11 25)(10 34 12 24)(41 80 51 70)(42 79 52 69)(43 78 53 68)(44 77 54 67)(45 76 55 66)(46 75 56 65)(47 74 57 64)(48 73 58 63)(49 72 59 62)(50 71 60 61)(81 115 91 105)(82 114 92 104)(83 113 93 103)(84 112 94 102)(85 111 95 101)(86 120 96 110)(87 119 97 109)(88 118 98 108)(89 117 99 107)(90 116 100 106)(121 160 131 150)(122 159 132 149)(123 158 133 148)(124 157 134 147)(125 156 135 146)(126 155 136 145)(127 154 137 144)(128 153 138 143)(129 152 139 142)(130 151 140 141)
(1 23)(2 24)(3 25)(4 26)(5 27)(6 28)(7 29)(8 30)(9 21)(10 22)(11 31)(12 32)(13 33)(14 34)(15 35)(16 36)(17 37)(18 38)(19 39)(20 40)(41 66)(42 67)(43 68)(44 69)(45 70)(46 61)(47 62)(48 63)(49 64)(50 65)(51 76)(52 77)(53 78)(54 79)(55 80)(56 71)(57 72)(58 73)(59 74)(60 75)(81 101)(82 102)(83 103)(84 104)(85 105)(86 106)(87 107)(88 108)(89 109)(90 110)(91 111)(92 112)(93 113)(94 114)(95 115)(96 116)(97 117)(98 118)(99 119)(100 120)(121 146)(122 147)(123 148)(124 149)(125 150)(126 141)(127 142)(128 143)(129 144)(130 145)(131 156)(132 157)(133 158)(134 159)(135 160)(136 151)(137 152)(138 153)(139 154)(140 155)

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

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

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

50 conjugacy classes

class 1 2A2B2C2D2E2F2G4A4B4C4D4E4F4G4H4I···4N5A5B10A···10F10G10H10I10J10K10L20A···20H20I···20N
order12222222444444444···45510···1010101010101020···2020···20
size1111441010224444101020···20222···24444884···48···8

50 irreducible representations

dim1111111111111122222244444
type++++++++++++++++++++--
imageC1C2C2C2C2C2C2C2C2C2C2C2C2C2D5C4○D4D10D10D10D102+ 1+42- 1+4D46D10D5×C4○D4D4.10D10
kernelC10.632+ 1+4Dic5.14D4C23.D10Dic54D4D10.12D4Dic5.Q8C4.Dic10D5×C4⋊C4D10⋊Q8C20.48D4C4×C5⋊D4C23.18D10C202D4C5×C22.D4C22.D4D10C22⋊C4C4⋊C4C22×C4C2×D4C10C10C2C2C2
# reps1121211111111124642211444

Matrix representation of C10.632+ 1+4 in GL8(𝔽41)

3434000000
71000000
0035340000
00600000
0000343500
00007000
0000003435
00000070
,
32027270000
0321400000
06900000
3535090000
0000380250
0000038025
000016030
000001603
,
320000000
032000000
003200000
000320000
000016030
000001603
0000380250
0000038025
,
400330000
7123200000
00670000
0036350000
000032100
0000213800
000000321
0000002138
,
400330000
0403800000
00100000
00010000
0000173500
000072400
0000001735
000000724

G:=sub<GL(8,GF(41))| [34,7,0,0,0,0,0,0,34,1,0,0,0,0,0,0,0,0,35,6,0,0,0,0,0,0,34,0,0,0,0,0,0,0,0,0,34,7,0,0,0,0,0,0,35,0,0,0,0,0,0,0,0,0,34,7,0,0,0,0,0,0,35,0],[32,0,0,35,0,0,0,0,0,32,6,35,0,0,0,0,27,14,9,0,0,0,0,0,27,0,0,9,0,0,0,0,0,0,0,0,38,0,16,0,0,0,0,0,0,38,0,16,0,0,0,0,25,0,3,0,0,0,0,0,0,25,0,3],[32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,16,0,38,0,0,0,0,0,0,16,0,38,0,0,0,0,3,0,25,0,0,0,0,0,0,3,0,25],[40,7,0,0,0,0,0,0,0,1,0,0,0,0,0,0,3,23,6,36,0,0,0,0,3,20,7,35,0,0,0,0,0,0,0,0,3,21,0,0,0,0,0,0,21,38,0,0,0,0,0,0,0,0,3,21,0,0,0,0,0,0,21,38],[40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,3,38,1,0,0,0,0,0,3,0,0,1,0,0,0,0,0,0,0,0,17,7,0,0,0,0,0,0,35,24,0,0,0,0,0,0,0,0,17,7,0,0,0,0,0,0,35,24] >;

C10.632+ 1+4 in GAP, Magma, Sage, TeX

C_{10}._{63}2_+^{1+4}
% in TeX

G:=Group("C10.63ES+(2,2)");
// GroupNames label

G:=SmallGroup(320,1332);
// by ID

G=gap.SmallGroup(320,1332);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,219,184,675,297,12550]);
// Polycyclic

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

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