Copied to
clipboard

G = C10.472+ 1+4order 320 = 26·5

47th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.472+ 1+4, C4⋊D422D5, C207D434C2, C202D427C2, C20⋊D419C2, C4⋊C4.185D10, (D4×Dic5)⋊26C2, (C2×D4).95D10, D208C422C2, (C2×C20).45C23, C22⋊C4.11D10, C4.Dic1021C2, Dic5⋊D417C2, C20.206(C4○D4), C4.69(D42D5), (C2×C10).163C24, (C22×C4).230D10, D10.12D422C2, C2.49(D46D10), C2.31(D48D10), C23.23(C22×D5), (D4×C10).128C22, (C2×D20).151C22, C22.D2013C2, C4⋊Dic5.210C22, (C2×Dic5).80C23, (C22×D5).70C23, C22.184(C23×D5), D10⋊C4.17C22, C23.21D1028C2, (C22×C20).246C22, (C22×C10).191C23, C54(C22.34C24), (C4×Dic5).107C22, C10.D4.21C22, C23.D5.113C22, (C22×Dic5).115C22, (C5×C4⋊D4)⋊25C2, C10.87(C2×C4○D4), (C2×C4×D5).98C22, C2.42(C2×D42D5), (C2×C4).41(C22×D5), (C5×C4⋊C4).150C22, (C2×C5⋊D4).35C22, (C5×C22⋊C4).19C22, SmallGroup(320,1291)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C10.472+ 1+4
C1C5C10C2×C10C22×D5C2×C4×D5D10.12D4 — C10.472+ 1+4
C5C2×C10 — C10.472+ 1+4
C1C22C4⋊D4

Generators and relations for C10.472+ 1+4
 G = < a,b,c,d,e | a10=b4=e2=1, c2=a5, d2=a5b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc-1=a5b-1, dbd-1=a5b, be=eb, dcd-1=ece=a5c, ede=a5b2d >

Subgroups: 910 in 240 conjugacy classes, 95 normal (43 characteristic)
C1, C2 [×3], C2 [×5], C4 [×2], C4 [×9], C22, C22 [×15], C5, C2×C4 [×2], C2×C4 [×2], C2×C4 [×12], D4 [×12], C23, C23 [×2], C23 [×2], D5 [×2], C10 [×3], C10 [×3], C42 [×2], C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4, C4⋊C4 [×7], C22×C4, C22×C4 [×4], C2×D4, C2×D4 [×2], C2×D4 [×7], Dic5 [×6], C20 [×2], C20 [×3], D10 [×6], C2×C10, C2×C10 [×9], C42⋊C2, C4×D4 [×2], C4⋊D4, C4⋊D4 [×5], C22.D4 [×4], C42.C2, C41D4, C4×D5 [×2], D20 [×2], C2×Dic5 [×4], C2×Dic5 [×2], C2×Dic5 [×2], C5⋊D4 [×6], C2×C20 [×2], C2×C20 [×2], C2×C20 [×2], C5×D4 [×4], C22×D5 [×2], C22×C10, C22×C10 [×2], C22.34C24, C4×Dic5 [×2], C10.D4 [×2], C4⋊Dic5 [×3], C4⋊Dic5 [×2], D10⋊C4 [×4], C23.D5 [×2], C23.D5 [×2], C5×C22⋊C4 [×2], C5×C4⋊C4, C2×C4×D5 [×2], C2×D20, C22×Dic5 [×2], C2×C5⋊D4 [×6], C22×C20, D4×C10, D4×C10 [×2], D10.12D4 [×2], C22.D20 [×2], C4.Dic10, D208C4, C23.21D10, C207D4, D4×Dic5, C202D4 [×2], Dic5⋊D4 [×2], C20⋊D4, C5×C4⋊D4, C10.472+ 1+4
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], D5, C4○D4 [×2], C24, D10 [×7], C2×C4○D4, 2+ 1+4 [×2], C22×D5 [×7], C22.34C24, D42D5 [×2], C23×D5, C2×D42D5, D46D10, D48D10, C10.472+ 1+4

Smallest permutation representation of C10.472+ 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)
(1 138 18 123)(2 139 19 124)(3 140 20 125)(4 131 11 126)(5 132 12 127)(6 133 13 128)(7 134 14 129)(8 135 15 130)(9 136 16 121)(10 137 17 122)(21 156 36 141)(22 157 37 142)(23 158 38 143)(24 159 39 144)(25 160 40 145)(26 151 31 146)(27 152 32 147)(28 153 33 148)(29 154 34 149)(30 155 35 150)(41 96 56 81)(42 97 57 82)(43 98 58 83)(44 99 59 84)(45 100 60 85)(46 91 51 86)(47 92 52 87)(48 93 53 88)(49 94 54 89)(50 95 55 90)(61 116 76 101)(62 117 77 102)(63 118 78 103)(64 119 79 104)(65 120 80 105)(66 111 71 106)(67 112 72 107)(68 113 73 108)(69 114 74 109)(70 115 75 110)
(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 75 51 65)(42 74 52 64)(43 73 53 63)(44 72 54 62)(45 71 55 61)(46 80 56 70)(47 79 57 69)(48 78 58 68)(49 77 59 67)(50 76 60 66)(81 120 91 110)(82 119 92 109)(83 118 93 108)(84 117 94 107)(85 116 95 106)(86 115 96 105)(87 114 97 104)(88 113 98 103)(89 112 99 102)(90 111 100 101)(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)(81 106)(82 107)(83 108)(84 109)(85 110)(86 101)(87 102)(88 103)(89 104)(90 105)(91 116)(92 117)(93 118)(94 119)(95 120)(96 111)(97 112)(98 113)(99 114)(100 115)(121 141)(122 142)(123 143)(124 144)(125 145)(126 146)(127 147)(128 148)(129 149)(130 150)(131 151)(132 152)(133 153)(134 154)(135 155)(136 156)(137 157)(138 158)(139 159)(140 160)

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

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

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

50 conjugacy classes

class 1 2A2B2C2D2E2F2G2H4A4B4C4D4E4F4G4H4I4J4K4L4M5A5B10A···10F10G10H10I10J10K10L10M10N20A···20H20I20J20K20L
order12222222244444444444445510···10101010101010101020···2020202020
size11114442020224441010101020202020222···2444488884···48888

50 irreducible representations

dim1111111111112222224444
type++++++++++++++++++-+
imageC1C2C2C2C2C2C2C2C2C2C2C2D5C4○D4D10D10D10D102+ 1+4D42D5D46D10D48D10
kernelC10.472+ 1+4D10.12D4C22.D20C4.Dic10D208C4C23.21D10C207D4D4×Dic5C202D4Dic5⋊D4C20⋊D4C5×C4⋊D4C4⋊D4C20C22⋊C4C4⋊C4C22×C4C2×D4C10C4C2C2
# reps1221111122112442262444

Matrix representation of C10.472+ 1+4 in GL8(𝔽41)

400000000
040000000
00770000
0034400000
00001000
00000100
00000010
00000001
,
19000000
040000000
004000000
000400000
0000340380
0000034038
00003070
00000307
,
90000000
3932000000
00100000
00010000
00003070
00000307
0000340380
0000034038
,
19000000
1840000000
004000000
00710000
00000100
000040000
00000001
000000400
,
19000000
040000000
004000000
000400000
00000100
00001000
00000001
00000010

G:=sub<GL(8,GF(41))| [40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,7,34,0,0,0,0,0,0,7,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,9,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,34,0,3,0,0,0,0,0,0,34,0,3,0,0,0,0,38,0,7,0,0,0,0,0,0,38,0,7],[9,39,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,3,0,34,0,0,0,0,0,0,3,0,34,0,0,0,0,7,0,38,0,0,0,0,0,0,7,0,38],[1,18,0,0,0,0,0,0,9,40,0,0,0,0,0,0,0,0,40,7,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,9,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;

C10.472+ 1+4 in GAP, Magma, Sage, TeX

C_{10}._{47}2_+^{1+4}
% in TeX

G:=Group("C10.47ES+(2,2)");
// GroupNames label

G:=SmallGroup(320,1291);
// by ID

G=gap.SmallGroup(320,1291);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,758,219,675,570,297,12550]);
// Polycyclic

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

׿
×
𝔽