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G = C10.572+ 1+4order 320 = 26·5

57th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.572+ 1+4, C10.782- 1+4, C22⋊Q822D5, C4⋊C4.100D10, (C2×Q8).78D10, D103Q824C2, C207D4.19C2, (C2×C20).65C23, C22⋊C4.65D10, C4.Dic1026C2, Dic54D416C2, (C2×C10).189C24, (C2×D20).33C22, (C22×C4).251D10, D10.13D423C2, C2.59(D46D10), C22.D2017C2, C4⋊Dic5.221C22, (Q8×C10).118C22, C22.5(Q82D5), (C2×Dic5).95C23, (C22×D5).80C23, C22.210(C23×D5), C23.197(C22×D5), D10⋊C4.72C22, (C22×C10).217C23, (C22×C20).317C22, C55(C22.33C24), (C4×Dic5).124C22, C2.38(D4.10D10), C10.D4.119C22, (C22×Dic5).125C22, C4⋊C4⋊D524C2, (C5×C22⋊Q8)⋊25C2, C10.117(C2×C4○D4), C2.21(C2×Q82D5), (C2×C4×D5).114C22, (C2×C10).29(C4○D4), (C2×C10.D4)⋊30C2, (C5×C4⋊C4).169C22, (C2×C4).186(C22×D5), (C2×C5⋊D4).41C22, (C5×C22⋊C4).44C22, SmallGroup(320,1317)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C10.572+ 1+4
C1C5C10C2×C10C22×D5C2×C5⋊D4Dic54D4 — C10.572+ 1+4
C5C2×C10 — C10.572+ 1+4
C1C22C22⋊Q8

Generators and relations for C10.572+ 1+4
 G = < a,b,c,d,e | a10=b4=c2=1, d2=a5b2, e2=b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc=a5b-1, dbd-1=ebe-1=a5b, cd=dc, ce=ec, ede-1=a5b2d >

Subgroups: 766 in 218 conjugacy classes, 95 normal (31 characteristic)
C1, C2 [×3], C2 [×4], C4 [×12], C22, C22 [×2], C22 [×8], C5, C2×C4 [×2], C2×C4 [×4], C2×C4 [×12], D4 [×5], Q8, C23, C23 [×2], D5 [×2], C10 [×3], C10 [×2], C42 [×2], C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4, C4⋊C4 [×2], C4⋊C4 [×11], C22×C4, C22×C4 [×4], C2×D4 [×3], C2×Q8, Dic5 [×6], C20 [×6], D10 [×6], C2×C10, C2×C10 [×2], C2×C10 [×2], C2×C4⋊C4, C4×D4 [×2], C4⋊D4, C22⋊Q8, C22⋊Q8 [×2], C22.D4 [×4], C42.C2 [×2], C422C2 [×2], C4×D5 [×2], D20, C2×Dic5 [×6], C2×Dic5 [×3], C5⋊D4 [×4], C2×C20 [×2], C2×C20 [×4], C2×C20, C5×Q8, C22×D5 [×2], C22×C10, C22.33C24, C4×Dic5 [×2], C10.D4 [×6], C4⋊Dic5, C4⋊Dic5 [×4], D10⋊C4 [×8], C5×C22⋊C4 [×2], C5×C4⋊C4, C5×C4⋊C4 [×2], C2×C4×D5 [×2], C2×D20, C22×Dic5 [×2], C2×C5⋊D4 [×2], C22×C20, Q8×C10, Dic54D4 [×2], C22.D20 [×2], C4.Dic10 [×2], D10.13D4 [×2], C4⋊C4⋊D5 [×2], C2×C10.D4, C207D4, D103Q8 [×2], C5×C22⋊Q8, C10.572+ 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, Q82D5 [×2], C23×D5, D46D10, C2×Q82D5, D4.10D10, C10.572+ 1+4

Smallest permutation representation of C10.572+ 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)
(1 153 28 11)(2 154 29 12)(3 155 30 13)(4 156 21 14)(5 157 22 15)(6 158 23 16)(7 159 24 17)(8 160 25 18)(9 151 26 19)(10 152 27 20)(31 131 43 143)(32 132 44 144)(33 133 45 145)(34 134 46 146)(35 135 47 147)(36 136 48 148)(37 137 49 149)(38 138 50 150)(39 139 41 141)(40 140 42 142)(51 116 63 128)(52 117 64 129)(53 118 65 130)(54 119 66 121)(55 120 67 122)(56 111 68 123)(57 112 69 124)(58 113 70 125)(59 114 61 126)(60 115 62 127)(71 108 83 96)(72 109 84 97)(73 110 85 98)(74 101 86 99)(75 102 87 100)(76 103 88 91)(77 104 89 92)(78 105 90 93)(79 106 81 94)(80 107 82 95)
(1 105)(2 106)(3 107)(4 108)(5 109)(6 110)(7 101)(8 102)(9 103)(10 104)(11 85)(12 86)(13 87)(14 88)(15 89)(16 90)(17 81)(18 82)(19 83)(20 84)(21 96)(22 97)(23 98)(24 99)(25 100)(26 91)(27 92)(28 93)(29 94)(30 95)(31 111)(32 112)(33 113)(34 114)(35 115)(36 116)(37 117)(38 118)(39 119)(40 120)(41 121)(42 122)(43 123)(44 124)(45 125)(46 126)(47 127)(48 128)(49 129)(50 130)(51 131)(52 132)(53 133)(54 134)(55 135)(56 136)(57 137)(58 138)(59 139)(60 140)(61 141)(62 142)(63 143)(64 144)(65 145)(66 146)(67 147)(68 148)(69 149)(70 150)(71 151)(72 152)(73 153)(74 154)(75 155)(76 156)(77 157)(78 158)(79 159)(80 160)
(1 11 23 158)(2 20 24 157)(3 19 25 156)(4 18 26 155)(5 17 27 154)(6 16 28 153)(7 15 29 152)(8 14 30 151)(9 13 21 160)(10 12 22 159)(31 135 48 142)(32 134 49 141)(33 133 50 150)(34 132 41 149)(35 131 42 148)(36 140 43 147)(37 139 44 146)(38 138 45 145)(39 137 46 144)(40 136 47 143)(51 122 68 115)(52 121 69 114)(53 130 70 113)(54 129 61 112)(55 128 62 111)(56 127 63 120)(57 126 64 119)(58 125 65 118)(59 124 66 117)(60 123 67 116)(71 102 88 95)(72 101 89 94)(73 110 90 93)(74 109 81 92)(75 108 82 91)(76 107 83 100)(77 106 84 99)(78 105 85 98)(79 104 86 97)(80 103 87 96)
(1 38 28 50)(2 39 29 41)(3 40 30 42)(4 31 21 43)(5 32 22 44)(6 33 23 45)(7 34 24 46)(8 35 25 47)(9 36 26 48)(10 37 27 49)(11 145 153 133)(12 146 154 134)(13 147 155 135)(14 148 156 136)(15 149 157 137)(16 150 158 138)(17 141 159 139)(18 142 160 140)(19 143 151 131)(20 144 152 132)(51 83 63 71)(52 84 64 72)(53 85 65 73)(54 86 66 74)(55 87 67 75)(56 88 68 76)(57 89 69 77)(58 90 70 78)(59 81 61 79)(60 82 62 80)(91 128 103 116)(92 129 104 117)(93 130 105 118)(94 121 106 119)(95 122 107 120)(96 123 108 111)(97 124 109 112)(98 125 110 113)(99 126 101 114)(100 127 102 115)

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

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

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

50 conjugacy classes

class 1 2A2B2C2D2E2F2G4A···4F4G4H4I4J4K4L4M4N5A5B10A···10F10G10H10I10J20A···20H20I···20P
order122222224···4444444445510···101010101020···2020···20
size11112220204···41010101020202020222···244444···48···8

50 irreducible representations

dim111111111122222244444
type++++++++++++++++-+-
imageC1C2C2C2C2C2C2C2C2C2D5C4○D4D10D10D10D102+ 1+42- 1+4Q82D5D46D10D4.10D10
kernelC10.572+ 1+4Dic54D4C22.D20C4.Dic10D10.13D4C4⋊C4⋊D5C2×C10.D4C207D4D103Q8C5×C22⋊Q8C22⋊Q8C2×C10C22⋊C4C4⋊C4C22×C4C2×Q8C10C10C22C2C2
# reps122222112124462211444

Matrix representation of C10.572+ 1+4 in GL8(𝔽41)

3434000000
71000000
0034340000
00710000
000003500
000073400
000000035
000000734
,
0030320000
009110000
3032000000
911000000
0000150260
0000015026
0000260260
0000026026
,
400000000
040000000
004000000
000400000
000040314031
0000391391
00004031110
0000391240
,
0030320000
0027110000
3032000000
2711000000
000018152326
000018232318
000023262326
000023182318
,
3032000000
911000000
001190000
0032300000
0000112800
0000223000
0000001128
0000002230

G:=sub<GL(8,GF(41))| [34,7,0,0,0,0,0,0,34,1,0,0,0,0,0,0,0,0,34,7,0,0,0,0,0,0,34,1,0,0,0,0,0,0,0,0,0,7,0,0,0,0,0,0,35,34,0,0,0,0,0,0,0,0,0,7,0,0,0,0,0,0,35,34],[0,0,30,9,0,0,0,0,0,0,32,11,0,0,0,0,30,9,0,0,0,0,0,0,32,11,0,0,0,0,0,0,0,0,0,0,15,0,26,0,0,0,0,0,0,15,0,26,0,0,0,0,26,0,26,0,0,0,0,0,0,26,0,26],[40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,39,40,39,0,0,0,0,31,1,31,1,0,0,0,0,40,39,1,2,0,0,0,0,31,1,10,40],[0,0,30,27,0,0,0,0,0,0,32,11,0,0,0,0,30,27,0,0,0,0,0,0,32,11,0,0,0,0,0,0,0,0,0,0,18,18,23,23,0,0,0,0,15,23,26,18,0,0,0,0,23,23,23,23,0,0,0,0,26,18,26,18],[30,9,0,0,0,0,0,0,32,11,0,0,0,0,0,0,0,0,11,32,0,0,0,0,0,0,9,30,0,0,0,0,0,0,0,0,11,22,0,0,0,0,0,0,28,30,0,0,0,0,0,0,0,0,11,22,0,0,0,0,0,0,28,30] >;

C10.572+ 1+4 in GAP, Magma, Sage, TeX

C_{10}._{57}2_+^{1+4}
% in TeX

G:=Group("C10.57ES+(2,2)");
// GroupNames label

G:=SmallGroup(320,1317);
// by ID

G=gap.SmallGroup(320,1317);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,477,387,100,675,409,80,12550]);
// Polycyclic

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

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