Copied to
clipboard

G = C10.102+ 1+4order 320 = 26·5

10th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.102+ 1+4, C5⋊D44Q8, C20⋊Q810C2, C51(D43Q8), C4⋊C4.264D10, D102Q89C2, D10⋊Q82C2, C22.8(Q8×D5), D10.19(C2×Q8), Dic53Q89C2, C4.92(C4○D20), (C2×C10).55C24, Dic5.20(C2×Q8), C20.194(C4○D4), C20.48D418C2, C10.26(C22×Q8), (C2×C20).138C23, Dic5.Q81C2, (C22×C4).180D10, C2.13(D46D10), C22.89(C23×D5), C4⋊Dic5.192C22, C23.227(C22×D5), C23.D5.88C22, D10⋊C4.94C22, (C22×C10).404C23, (C22×C20).103C22, (C4×Dic5).212C22, (C2×Dic5).201C23, (C22×D5).170C23, (C2×Dic10).147C22, C10.D4.149C22, C2.9(C2×Q8×D5), (D5×C4⋊C4)⋊10C2, (C2×C4⋊C4)⋊20D5, (C10×C4⋊C4)⋊17C2, (C4×C5⋊D4).3C2, C10.22(C2×C4○D4), C2.24(C2×C4○D20), (C2×C10).95(C2×Q8), (C2×C4×D5).242C22, (C5×C4⋊C4).297C22, (C2×C4).573(C22×D5), (C2×C5⋊D4).159C22, SmallGroup(320,1183)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C10.102+ 1+4
C1C5C10C2×C10C22×D5C2×C4×D5D5×C4⋊C4 — C10.102+ 1+4
C5C2×C10 — C10.102+ 1+4
C1C22C2×C4⋊C4

Generators and relations for C10.102+ 1+4
 G = < a,b,c,d,e | a10=b4=c2=1, d2=b2, e2=a5, bab-1=a-1, ac=ca, ad=da, ae=ea, cbc=a5b-1, dbd-1=a5b, be=eb, cd=dc, ce=ec, ede-1=b2d >

Subgroups: 726 in 228 conjugacy classes, 107 normal (43 characteristic)
C1, C2 [×3], C2 [×4], C4 [×2], C4 [×13], C22, C22 [×2], C22 [×6], C5, C2×C4 [×2], C2×C4 [×4], C2×C4 [×15], D4 [×4], Q8 [×4], C23, C23, D5 [×2], C10 [×3], C10 [×2], C42 [×3], C22⋊C4 [×6], C4⋊C4 [×2], C4⋊C4 [×2], C4⋊C4 [×12], C22×C4, C22×C4 [×2], C22×C4 [×3], C2×D4, C2×Q8 [×3], Dic5 [×2], Dic5 [×6], C20 [×2], C20 [×5], D10 [×2], D10 [×2], C2×C10, C2×C10 [×2], C2×C10 [×2], C2×C4⋊C4, C2×C4⋊C4, C4×D4 [×3], C4×Q8, C22⋊Q8 [×6], C42.C2 [×2], C4⋊Q8, Dic10 [×4], C4×D5 [×4], C2×Dic5 [×3], C2×Dic5 [×4], C5⋊D4 [×4], C2×C20 [×2], C2×C20 [×4], C2×C20 [×4], C22×D5, C22×C10, D43Q8, C4×Dic5, C4×Dic5 [×2], C10.D4, C10.D4 [×8], C4⋊Dic5, C4⋊Dic5 [×2], D10⋊C4, D10⋊C4 [×2], C23.D5, C23.D5 [×2], C5×C4⋊C4 [×2], C5×C4⋊C4 [×2], C2×Dic10, C2×Dic10 [×2], C2×C4×D5, C2×C4×D5 [×2], C2×C5⋊D4, C22×C20, C22×C20 [×2], Dic53Q8, C20⋊Q8, Dic5.Q8 [×2], D5×C4⋊C4, D10⋊Q8 [×2], D102Q8, C20.48D4, C20.48D4 [×2], C4×C5⋊D4, C4×C5⋊D4 [×2], C10×C4⋊C4, C10.102+ 1+4
Quotients: C1, C2 [×15], C22 [×35], Q8 [×4], C23 [×15], D5, C2×Q8 [×6], C4○D4 [×2], C24, D10 [×7], C22×Q8, C2×C4○D4, 2+ 1+4, C22×D5 [×7], D43Q8, C4○D20 [×2], Q8×D5 [×2], C23×D5, C2×C4○D20, D46D10, C2×Q8×D5, C10.102+ 1+4

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

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

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

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

65 conjugacy classes

class 1 2A2B2C2D2E2F2G4A···4F4G4H4I4J4K4L···4Q5A5B10A···10N20A···20X
order122222224···4444444···45510···1020···20
size11112210102···2444101020···20222···24···4

65 irreducible representations

dim1111111111222222444
type++++++++++-++++-
imageC1C2C2C2C2C2C2C2C2C2Q8D5C4○D4D10D10C4○D202+ 1+4Q8×D5D46D10
kernelC10.102+ 1+4Dic53Q8C20⋊Q8Dic5.Q8D5×C4⋊C4D10⋊Q8D102Q8C20.48D4C4×C5⋊D4C10×C4⋊C4C5⋊D4C2×C4⋊C4C20C4⋊C4C22×C4C4C10C22C2
# reps11121213314248616144

Matrix representation of C10.102+ 1+4 in GL6(𝔽41)

4000000
0400000
00403500
0063500
0000400
0000040
,
910000
2320000
0035600
001600
0000321
00002138
,
4090000
010000
001000
000100
0000400
0000040
,
1320000
0400000
001000
000100
00002138
00003820
,
900000
090000
0040000
0004000
00003820
0000203

G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,6,0,0,0,0,35,35,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[9,2,0,0,0,0,1,32,0,0,0,0,0,0,35,1,0,0,0,0,6,6,0,0,0,0,0,0,3,21,0,0,0,0,21,38],[40,0,0,0,0,0,9,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,32,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,21,38,0,0,0,0,38,20],[9,0,0,0,0,0,0,9,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,38,20,0,0,0,0,20,3] >;

C10.102+ 1+4 in GAP, Magma, Sage, TeX

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

G:=Group("C10.10ES+(2,2)");
// GroupNames label

G:=SmallGroup(320,1183);
// by ID

G=gap.SmallGroup(320,1183);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,387,100,1571,12550]);
// Polycyclic

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

׿
×
𝔽