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G = C10.852- 1+4order 320 = 26·5

40th non-split extension by C10 of 2- 1+4 acting via 2- 1+4/C4○D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.852- 1+4, C10.1232+ 1+4, C4⋊C4.108D10, (D4×Dic5)⋊29C2, D102Q833C2, (C2×D4).167D10, C22⋊C4.69D10, C4.Dic1030C2, Dic54D426C2, (C2×C20).183C23, (C2×C10).209C24, Dic5⋊D4.3C2, (C22×C4).262D10, C22.D414D5, D10.12D437C2, C2.45(D48D10), C23.33(C22×D5), Dic5.Q830C2, (D4×C10).147C22, D10⋊C4.9C22, C23.23D108C2, C22.D2023C2, C23.D1035C2, C4⋊Dic5.313C22, (C22×C10).41C23, (C22×C20).87C22, (C22×D5).90C23, C22.230(C23×D5), Dic5.14D435C2, C23.D5.47C22, C22.12(D42D5), C57(C22.33C24), (C4×Dic5).136C22, (C2×Dic5).108C23, C10.D4.10C22, C2.46(D4.10D10), (C2×Dic10).177C22, (C22×Dic5).135C22, C4⋊C4⋊D531C2, (C2×C4⋊Dic5)⋊27C2, C10.92(C2×C4○D4), C2.54(C2×D42D5), (C2×C4×D5).125C22, (C2×C10).48(C4○D4), (C5×C4⋊C4).182C22, (C2×C4).190(C22×D5), (C2×C5⋊D4).53C22, (C5×C22.D4)⋊17C2, (C5×C22⋊C4).57C22, SmallGroup(320,1337)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C10.852- 1+4
C1C5C10C2×C10C22×D5C2×C5⋊D4Dic54D4 — C10.852- 1+4
C5C2×C10 — C10.852- 1+4
C1C22C22.D4

Generators and relations for C10.852- 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=b-1, dbd-1=ebe-1=a5b, cd=dc, ce=ec, ede-1=b2d >

Subgroups: 734 in 218 conjugacy classes, 95 normal (91 characteristic)
C1, C2 [×3], C2 [×4], C4 [×12], C22, C22 [×2], C22 [×8], C5, C2×C4 [×5], C2×C4 [×13], D4 [×5], Q8, C23 [×2], C23, D5, C10 [×3], C10 [×3], C42 [×2], C22⋊C4 [×3], C22⋊C4 [×7], C4⋊C4 [×2], C4⋊C4 [×12], C22×C4, C22×C4 [×4], C2×D4, C2×D4 [×2], C2×Q8, Dic5 [×7], C20 [×5], D10 [×3], C2×C10, C2×C10 [×2], C2×C10 [×5], C2×C4⋊C4, C4×D4 [×2], C4⋊D4, C22⋊Q8 [×3], C22.D4, C22.D4 [×3], C42.C2 [×2], C422C2 [×2], Dic10, C4×D5, C2×Dic5 [×7], C2×Dic5 [×3], C5⋊D4 [×3], C2×C20 [×5], C2×C20 [×2], C5×D4 [×2], C22×D5, C22×C10 [×2], C22.33C24, C4×Dic5 [×2], C10.D4 [×6], C4⋊Dic5 [×6], D10⋊C4 [×4], C23.D5 [×3], C5×C22⋊C4 [×3], C5×C4⋊C4 [×2], C2×Dic10, C2×C4×D5, C22×Dic5 [×3], C2×C5⋊D4 [×2], C22×C20, D4×C10, Dic5.14D4 [×2], C23.D10, Dic54D4, D10.12D4, C22.D20, Dic5.Q8, C4.Dic10, D102Q8, C4⋊C4⋊D5, C2×C4⋊Dic5, C23.23D10, D4×Dic5, Dic5⋊D4, C5×C22.D4, C10.852- 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, D42D5 [×2], C23×D5, C2×D42D5, D48D10, D4.10D10, C10.852- 1+4

Smallest permutation representation of C10.852- 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)
(1 158 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)(31 131 48 148)(32 132 49 149)(33 133 50 150)(34 134 41 141)(35 135 42 142)(36 136 43 143)(37 137 44 144)(38 138 45 145)(39 139 46 146)(40 140 47 147)(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)(71 108 88 91)(72 109 89 92)(73 110 90 93)(74 101 81 94)(75 102 82 95)(76 103 83 96)(77 104 84 97)(78 105 85 98)(79 106 86 99)(80 107 87 100)
(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 16 28 158)(2 15 29 157)(3 14 30 156)(4 13 21 155)(5 12 22 154)(6 11 23 153)(7 20 24 152)(8 19 25 151)(9 18 26 160)(10 17 27 159)(31 135 43 147)(32 134 44 146)(33 133 45 145)(34 132 46 144)(35 131 47 143)(36 140 48 142)(37 139 49 141)(38 138 50 150)(39 137 41 149)(40 136 42 148)(51 127 63 115)(52 126 64 114)(53 125 65 113)(54 124 66 112)(55 123 67 111)(56 122 68 120)(57 121 69 119)(58 130 70 118)(59 129 61 117)(60 128 62 116)(71 102 83 100)(72 101 84 99)(73 110 85 98)(74 109 86 97)(75 108 87 96)(76 107 88 95)(77 106 89 94)(78 105 90 93)(79 104 81 92)(80 103 82 91)
(1 33 23 50)(2 34 24 41)(3 35 25 42)(4 36 26 43)(5 37 27 44)(6 38 28 45)(7 39 29 46)(8 40 30 47)(9 31 21 48)(10 32 22 49)(11 145 158 138)(12 146 159 139)(13 147 160 140)(14 148 151 131)(15 149 152 132)(16 150 153 133)(17 141 154 134)(18 142 155 135)(19 143 156 136)(20 144 157 137)(51 88 68 71)(52 89 69 72)(53 90 70 73)(54 81 61 74)(55 82 62 75)(56 83 63 76)(57 84 64 77)(58 85 65 78)(59 86 66 79)(60 87 67 80)(91 123 108 116)(92 124 109 117)(93 125 110 118)(94 126 101 119)(95 127 102 120)(96 128 103 111)(97 129 104 112)(98 130 105 113)(99 121 106 114)(100 122 107 115)

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

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

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

50 conjugacy classes

class 1 2A2B2C2D2E2F2G4A···4E4F4G4H4I4J···4N5A5B10A···10F10G10H10I10J10K10L20A···20H20I···20N
order122222224···444444···45510···1010101010101020···2020···20
size1111224204···41010101020···20222···24444884···48···8

50 irreducible representations

dim11111111111111122222244444
type+++++++++++++++++++++--+-
imageC1C2C2C2C2C2C2C2C2C2C2C2C2C2C2D5C4○D4D10D10D10D102+ 1+42- 1+4D42D5D48D10D4.10D10
kernelC10.852- 1+4Dic5.14D4C23.D10Dic54D4D10.12D4C22.D20Dic5.Q8C4.Dic10D102Q8C4⋊C4⋊D5C2×C4⋊Dic5C23.23D10D4×Dic5Dic5⋊D4C5×C22.D4C22.D4C2×C10C22⋊C4C4⋊C4C22×C4C2×D4C10C10C22C2C2
# reps12111111111111124642211444

Matrix representation of C10.852- 1+4 in GL6(𝔽41)

4000000
0400000
007700
00344000
000077
00003440
,
0320000
900000
0030210
0003021
00210380
00021038
,
100000
010000
002625814
0016152733
008141516
0027332526
,
0320000
3200000
00380200
002132421
0020030
0024212038
,
010000
100000
0011900
00323000
0000119
00003230

G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,7,34,0,0,0,0,7,40,0,0,0,0,0,0,7,34,0,0,0,0,7,40],[0,9,0,0,0,0,32,0,0,0,0,0,0,0,3,0,21,0,0,0,0,3,0,21,0,0,21,0,38,0,0,0,0,21,0,38],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,26,16,8,27,0,0,25,15,14,33,0,0,8,27,15,25,0,0,14,33,16,26],[0,32,0,0,0,0,32,0,0,0,0,0,0,0,38,21,20,24,0,0,0,3,0,21,0,0,20,24,3,20,0,0,0,21,0,38],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,11,32,0,0,0,0,9,30,0,0,0,0,0,0,11,32,0,0,0,0,9,30] >;

C10.852- 1+4 in GAP, Magma, Sage, TeX

C_{10}._{85}2_-^{1+4}
% in TeX

G:=Group("C10.85ES-(2,2)");
// GroupNames label

G:=SmallGroup(320,1337);
// by ID

G=gap.SmallGroup(320,1337);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,477,387,100,675,409,136,12550]);
// 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=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=b^2*d>;
// generators/relations

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