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G = C10.1472+ 1+4order 320 = 26·5

56th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C4○D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.1472+ 1+4, C10.1082- 1+4, (C2×C20)⋊18D4, C202D443C2, C207D449C2, C20.431(C2×D4), D103Q845C2, (C2×D4).238D10, (C2×Q8).195D10, Dic5⋊D445C2, C20.48D449C2, (C2×C20).654C23, (C2×C10).319C24, C10.169(C22×D4), (C22×C4).289D10, C2.71(D48D10), (C2×D20).239C22, (D4×C10).315C22, C4⋊Dic5.393C22, (Q8×C10).245C22, C23.140(C22×D5), C22.328(C23×D5), C23.D5.77C22, D10⋊C4.79C22, (C22×C20).321C22, (C22×C10).245C23, C55(C22.31C24), (C2×Dic5).165C23, C10.D4.93C22, (C22×D5).140C23, C2.71(D4.10D10), (C2×Dic10).267C22, (C22×Dic5).168C22, (C2×C4○D4)⋊11D5, (C2×C4)⋊8(C5⋊D4), (C2×C4○D20)⋊33C2, (C10×C4○D4)⋊11C2, (C2×C4⋊Dic5)⋊48C2, (C2×C10).84(C2×D4), C4.101(C2×C5⋊D4), C22.2(C2×C5⋊D4), (C2×C4×D5).179C22, C2.42(C22×C5⋊D4), (C2×C4).641(C22×D5), (C2×C5⋊D4).82C22, SmallGroup(320,1505)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C10.1472+ 1+4
C1C5C10C2×C10C22×D5C2×C4×D5C2×C4○D20 — C10.1472+ 1+4
C5C2×C10 — C10.1472+ 1+4
C1C22C2×C4○D4

Generators and relations for C10.1472+ 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, ebe-1=a5b, dcd-1=a5c, ce=ec, ede-1=b2d >

Subgroups: 1022 in 294 conjugacy classes, 111 normal (29 characteristic)
C1, C2 [×3], C2 [×6], C4 [×4], C4 [×8], C22, C22 [×2], C22 [×14], C5, C2×C4 [×2], C2×C4 [×6], C2×C4 [×16], D4 [×16], Q8 [×4], C23, C23 [×2], C23 [×2], D5 [×2], C10 [×3], C10 [×4], C22⋊C4 [×8], C4⋊C4 [×8], C22×C4, C22×C4 [×2], C22×C4 [×4], C2×D4, C2×D4 [×2], C2×D4 [×7], C2×Q8, C2×Q8, C4○D4 [×8], Dic5 [×6], C20 [×4], C20 [×2], D10 [×6], C2×C10, C2×C10 [×2], C2×C10 [×8], C2×C4⋊C4, C4⋊D4 [×8], C22⋊Q8 [×4], C2×C4○D4, C2×C4○D4, Dic10 [×2], C4×D5 [×4], D20 [×2], C2×Dic5 [×6], C2×Dic5 [×2], C5⋊D4 [×8], C2×C20 [×2], C2×C20 [×6], C2×C20 [×4], C5×D4 [×6], C5×Q8 [×2], C22×D5 [×2], C22×C10, C22×C10 [×2], C22.31C24, C10.D4 [×4], C4⋊Dic5 [×4], D10⋊C4 [×4], C23.D5 [×4], C2×Dic10, C2×C4×D5 [×2], C2×D20, C4○D20 [×4], C22×Dic5 [×2], C2×C5⋊D4 [×6], C22×C20, C22×C20 [×2], D4×C10, D4×C10 [×2], Q8×C10, C5×C4○D4 [×4], C20.48D4 [×2], C2×C4⋊Dic5, C207D4 [×2], C202D4 [×2], Dic5⋊D4 [×4], D103Q8 [×2], C2×C4○D20, C10×C4○D4, C10.1472+ 1+4
Quotients: C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D5, C2×D4 [×6], C24, D10 [×7], C22×D4, 2+ 1+4, 2- 1+4, C5⋊D4 [×4], C22×D5 [×7], C22.31C24, C2×C5⋊D4 [×6], C23×D5, D48D10, D4.10D10, C22×C5⋊D4, C10.1472+ 1+4

Smallest permutation representation of C10.1472+ 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 28 50)(2 37 29 49)(3 36 30 48)(4 35 21 47)(5 34 22 46)(6 33 23 45)(7 32 24 44)(8 31 25 43)(9 40 26 42)(10 39 27 41)(11 133 153 145)(12 132 154 144)(13 131 155 143)(14 140 156 142)(15 139 157 141)(16 138 158 150)(17 137 159 149)(18 136 160 148)(19 135 151 147)(20 134 152 146)(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)(91 115 103 127)(92 114 104 126)(93 113 105 125)(94 112 106 124)(95 111 107 123)(96 120 108 122)(97 119 109 121)(98 118 110 130)(99 117 101 129)(100 116 102 128)
(1 45)(2 46)(3 47)(4 48)(5 49)(6 50)(7 41)(8 42)(9 43)(10 44)(11 145)(12 146)(13 147)(14 148)(15 149)(16 150)(17 141)(18 142)(19 143)(20 144)(21 36)(22 37)(23 38)(24 39)(25 40)(26 31)(27 32)(28 33)(29 34)(30 35)(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)(91 128)(92 129)(93 130)(94 121)(95 122)(96 123)(97 124)(98 125)(99 126)(100 127)(101 114)(102 115)(103 116)(104 117)(105 118)(106 119)(107 120)(108 111)(109 112)(110 113)(131 151)(132 152)(133 153)(134 154)(135 155)(136 156)(137 157)(138 158)(139 159)(140 160)
(1 78 28 90)(2 77 29 89)(3 76 30 88)(4 75 21 87)(5 74 22 86)(6 73 23 85)(7 72 24 84)(8 71 25 83)(9 80 26 82)(10 79 27 81)(11 93 153 105)(12 92 154 104)(13 91 155 103)(14 100 156 102)(15 99 157 101)(16 98 158 110)(17 97 159 109)(18 96 160 108)(19 95 151 107)(20 94 152 106)(31 60 43 62)(32 59 44 61)(33 58 45 70)(34 57 46 69)(35 56 47 68)(36 55 48 67)(37 54 49 66)(38 53 50 65)(39 52 41 64)(40 51 42 63)(111 147 123 135)(112 146 124 134)(113 145 125 133)(114 144 126 132)(115 143 127 131)(116 142 128 140)(117 141 129 139)(118 150 130 138)(119 149 121 137)(120 148 122 136)
(1 158 23 11)(2 159 24 12)(3 160 25 13)(4 151 26 14)(5 152 27 15)(6 153 28 16)(7 154 29 17)(8 155 30 18)(9 156 21 19)(10 157 22 20)(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)(51 111 68 128)(52 112 69 129)(53 113 70 130)(54 114 61 121)(55 115 62 122)(56 116 63 123)(57 117 64 124)(58 118 65 125)(59 119 66 126)(60 120 67 127)(71 91 88 108)(72 92 89 109)(73 93 90 110)(74 94 81 101)(75 95 82 102)(76 96 83 103)(77 97 84 104)(78 98 85 105)(79 99 86 106)(80 100 87 107)

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

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

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

62 conjugacy classes

class 1 2A2B2C2D2E2F2G2H2I4A4B4C4D4E4F4G···4L5A5B10A···10F10G···10R20A···20H20I···20T
order12222222224444444···45510···1010···1020···2020···20
size11112244202022224420···20222···24···42···24···4

62 irreducible representations

dim1111111112222224444
type+++++++++++++++-+-
imageC1C2C2C2C2C2C2C2C2D4D5D10D10D10C5⋊D42+ 1+42- 1+4D48D10D4.10D10
kernelC10.1472+ 1+4C20.48D4C2×C4⋊Dic5C207D4C202D4Dic5⋊D4D103Q8C2×C4○D20C10×C4○D4C2×C20C2×C4○D4C22×C4C2×D4C2×Q8C2×C4C10C10C2C2
# reps12122421142662161144

Matrix representation of C10.1472+ 1+4 in GL6(𝔽41)

4000000
0400000
00403500
0063500
00603435
00403570
,
0400000
100000
003535712
00353565
0012676
00411405
,
010000
100000
00003540
00404021
000010
00400350
,
0400000
100000
00262150
0025151826
00390292
00142412
,
010000
100000
001313326
0022026
001303028
002132537

G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,6,6,40,0,0,35,35,0,35,0,0,0,0,34,7,0,0,0,0,35,0],[0,1,0,0,0,0,40,0,0,0,0,0,0,0,35,35,12,4,0,0,35,35,6,11,0,0,7,6,7,40,0,0,12,5,6,5],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,40,0,0,0,40,0,0,0,0,35,2,1,35,0,0,40,1,0,0],[0,1,0,0,0,0,40,0,0,0,0,0,0,0,26,25,39,14,0,0,2,15,0,2,0,0,15,18,29,4,0,0,0,26,2,12],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,13,2,13,2,0,0,13,2,0,13,0,0,3,0,30,25,0,0,26,26,28,37] >;

C10.1472+ 1+4 in GAP, Magma, Sage, TeX

C_{10}._{147}2_+^{1+4}
% in TeX

G:=Group("C10.147ES+(2,2)");
// GroupNames label

G:=SmallGroup(320,1505);
// by ID

G=gap.SmallGroup(320,1505);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,758,675,570,297,12550]);
// 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,e*b*e^-1=a^5*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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