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G = C10.342+ 1+4order 320 = 26·5

34th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.342+ 1+4, C4⋊D48D5, C4⋊C4.90D10, (D4×Dic5)⋊17C2, Dic54D47C2, (C2×D4).153D10, (C2×C20).36C23, C22⋊C4.48D10, Dic5⋊D429C2, (C2×C10).145C24, (C22×C4).220D10, D10.12D416C2, C2.36(D46D10), Dic5.38(C4○D4), Dic5.Q811C2, (D4×C10).119C22, C22.1(D42D5), C23.D1015C2, C23.11D105C2, C4⋊Dic5.206C22, (C22×C10).16C23, (C2×Dic5).66C23, (C22×D5).63C23, C22.166(C23×D5), C23.179(C22×D5), C23.D5.22C22, D10⋊C4.13C22, C23.18D1020C2, (C22×C20).378C22, C56(C22.47C24), (C4×Dic5).100C22, C10.D4.16C22, (C22×Dic5).106C22, (C5×C4⋊D4)⋊9C2, (C4×C5⋊D4)⋊53C2, C2.36(D5×C4○D4), C4⋊C4⋊D512C2, C10.81(C2×C4○D4), C2.33(C2×D42D5), (C2×C4×D5).259C22, (C2×C10).21(C4○D4), (C2×C10.D4)⋊40C2, (C5×C4⋊C4).141C22, (C2×C4).293(C22×D5), (C2×C5⋊D4).26C22, (C5×C22⋊C4).10C22, SmallGroup(320,1273)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C10.342+ 1+4
C1C5C10C2×C10C2×Dic5C22×Dic5C2×C10.D4 — C10.342+ 1+4
C5C2×C10 — C10.342+ 1+4
C1C22C4⋊D4

Generators and relations for C10.342+ 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=b-1, dbd-1=ebe=a5b, cd=dc, ce=ec, ede=a5b2d >

Subgroups: 790 in 238 conjugacy classes, 97 normal (91 characteristic)
C1, C2 [×3], C2 [×5], C4 [×12], C22, C22 [×2], C22 [×11], C5, C2×C4 [×4], C2×C4 [×15], D4 [×10], C23 [×3], C23, D5, C10 [×3], C10 [×4], C42 [×3], C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4, C4⋊C4 [×9], C22×C4, C22×C4 [×5], C2×D4 [×3], C2×D4 [×3], Dic5 [×2], Dic5 [×6], C20 [×4], D10 [×3], C2×C10, C2×C10 [×2], C2×C10 [×8], C2×C4⋊C4, C42⋊C2, C4×D4 [×4], C4⋊D4, C4⋊D4 [×3], C22.D4 [×2], C42.C2, C422C2 [×2], C4×D5, C2×Dic5 [×7], C2×Dic5 [×6], C5⋊D4 [×5], C2×C20 [×4], C2×C20, C5×D4 [×5], C22×D5, C22×C10 [×3], C22.47C24, C4×Dic5 [×3], C10.D4 [×7], C4⋊Dic5 [×2], D10⋊C4 [×3], C23.D5 [×5], C5×C22⋊C4 [×2], C5×C4⋊C4, C2×C4×D5, C22×Dic5 [×4], C2×C5⋊D4 [×3], C22×C20, D4×C10 [×3], C23.11D10, C23.D10, Dic54D4, D10.12D4, Dic5.Q8, C4⋊C4⋊D5, C2×C10.D4, C4×C5⋊D4, D4×Dic5 [×2], C23.18D10, Dic5⋊D4 [×3], C5×C4⋊D4, C10.342+ 1+4
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], D5, C4○D4 [×4], C24, D10 [×7], C2×C4○D4 [×2], 2+ 1+4, C22×D5 [×7], C22.47C24, D42D5 [×2], C23×D5, C2×D42D5, D46D10, D5×C4○D4, C10.342+ 1+4

Smallest permutation representation of C10.342+ 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)
(1 110 25 93)(2 109 26 92)(3 108 27 91)(4 107 28 100)(5 106 29 99)(6 105 30 98)(7 104 21 97)(8 103 22 96)(9 102 23 95)(10 101 24 94)(11 85 158 78)(12 84 159 77)(13 83 160 76)(14 82 151 75)(15 81 152 74)(16 90 153 73)(17 89 154 72)(18 88 155 71)(19 87 156 80)(20 86 157 79)(31 122 48 115)(32 121 49 114)(33 130 50 113)(34 129 41 112)(35 128 42 111)(36 127 43 120)(37 126 44 119)(38 125 45 118)(39 124 46 117)(40 123 47 116)(51 147 68 140)(52 146 69 139)(53 145 70 138)(54 144 61 137)(55 143 62 136)(56 142 63 135)(57 141 64 134)(58 150 65 133)(59 149 66 132)(60 148 67 131)
(1 65 6 70)(2 64 7 69)(3 63 8 68)(4 62 9 67)(5 61 10 66)(11 125 16 130)(12 124 17 129)(13 123 18 128)(14 122 19 127)(15 121 20 126)(21 52 26 57)(22 51 27 56)(23 60 28 55)(24 59 29 54)(25 58 30 53)(31 87 36 82)(32 86 37 81)(33 85 38 90)(34 84 39 89)(35 83 40 88)(41 77 46 72)(42 76 47 71)(43 75 48 80)(44 74 49 79)(45 73 50 78)(91 135 96 140)(92 134 97 139)(93 133 98 138)(94 132 99 137)(95 131 100 136)(101 149 106 144)(102 148 107 143)(103 147 108 142)(104 146 109 141)(105 145 110 150)(111 160 116 155)(112 159 117 154)(113 158 118 153)(114 157 119 152)(115 156 120 151)
(1 118 25 125)(2 119 26 126)(3 120 27 127)(4 111 28 128)(5 112 29 129)(6 113 30 130)(7 114 21 121)(8 115 22 122)(9 116 23 123)(10 117 24 124)(11 70 158 53)(12 61 159 54)(13 62 160 55)(14 63 151 56)(15 64 152 57)(16 65 153 58)(17 66 154 59)(18 67 155 60)(19 68 156 51)(20 69 157 52)(31 91 48 108)(32 92 49 109)(33 93 50 110)(34 94 41 101)(35 95 42 102)(36 96 43 103)(37 97 44 104)(38 98 45 105)(39 99 46 106)(40 100 47 107)(71 143 88 136)(72 144 89 137)(73 145 90 138)(74 146 81 139)(75 147 82 140)(76 148 83 131)(77 149 84 132)(78 150 85 133)(79 141 86 134)(80 142 87 135)
(1 11)(2 12)(3 13)(4 14)(5 15)(6 16)(7 17)(8 18)(9 19)(10 20)(21 154)(22 155)(23 156)(24 157)(25 158)(26 159)(27 160)(28 151)(29 152)(30 153)(31 148)(32 149)(33 150)(34 141)(35 142)(36 143)(37 144)(38 145)(39 146)(40 147)(41 134)(42 135)(43 136)(44 137)(45 138)(46 139)(47 140)(48 131)(49 132)(50 133)(51 111)(52 112)(53 113)(54 114)(55 115)(56 116)(57 117)(58 118)(59 119)(60 120)(61 121)(62 122)(63 123)(64 124)(65 125)(66 126)(67 127)(68 128)(69 129)(70 130)(71 91)(72 92)(73 93)(74 94)(75 95)(76 96)(77 97)(78 98)(79 99)(80 100)(81 101)(82 102)(83 103)(84 104)(85 105)(86 106)(87 107)(88 108)(89 109)(90 110)

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

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

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

53 conjugacy classes

class 1 2A2B2C2D2E2F2G2H4A4B4C4D4E4F···4M4N4O4P5A5B10A···10F10G10H10I10J10K10L10M10N20A···20H20I20J20K20L
order122222222444444···44445510···10101010101010101020···2020202020
size11112244202244410···10202020222···2444488884···48888

53 irreducible representations

dim111111111111122222224444
type+++++++++++++++++++-
imageC1C2C2C2C2C2C2C2C2C2C2C2C2D5C4○D4C4○D4D10D10D10D102+ 1+4D42D5D46D10D5×C4○D4
kernelC10.342+ 1+4C23.11D10C23.D10Dic54D4D10.12D4Dic5.Q8C4⋊C4⋊D5C2×C10.D4C4×C5⋊D4D4×Dic5C23.18D10Dic5⋊D4C5×C4⋊D4C4⋊D4Dic5C2×C10C22⋊C4C4⋊C4C22×C4C2×D4C10C22C2C2
# reps111111111213124442261444

Matrix representation of C10.342+ 1+4 in GL6(𝔽41)

4000000
0400000
0040000
0004000
00004035
0000635
,
090000
900000
0040000
000100
0000356
000016
,
900000
0320000
0032000
0003200
0000356
000016
,
3200000
090000
0004000
0040000
0000400
0000040
,
100000
0400000
000900
0032000
000010
000001

G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,6,0,0,0,0,35,35],[0,9,0,0,0,0,9,0,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,35,1,0,0,0,0,6,6],[9,0,0,0,0,0,0,32,0,0,0,0,0,0,32,0,0,0,0,0,0,32,0,0,0,0,0,0,35,1,0,0,0,0,6,6],[32,0,0,0,0,0,0,9,0,0,0,0,0,0,0,40,0,0,0,0,40,0,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,40,0,0,0,0,0,0,0,32,0,0,0,0,9,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;

C10.342+ 1+4 in GAP, Magma, Sage, TeX

C_{10}._{34}2_+^{1+4}
% in TeX

G:=Group("C10.34ES+(2,2)");
// GroupNames label

G:=SmallGroup(320,1273);
// by ID

G=gap.SmallGroup(320,1273);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,758,100,794,297,12550]);
// Polycyclic

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

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