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G = C10.552+ 1+4order 320 = 26·5

55th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.552+ 1+4, C10.222- 1+4, C22⋊Q817D5, C4⋊C4.195D10, (C2×Q8).77D10, D10⋊Q823C2, D10⋊D4.2C2, C22⋊C4.20D10, Dic5⋊Q817C2, Dic53Q828C2, C20.23D415C2, (C2×C10).184C24, (C2×C20).628C23, (C22×C4).246D10, D10.13D421C2, C2.57(D46D10), Dic5.13(C4○D4), Dic5.5D426C2, (C2×D20).158C22, C23.D1024C2, C4⋊Dic5.219C22, (Q8×C10).114C22, (C22×D5).75C23, C22.205(C23×D5), C23.123(C22×D5), C23.D5.35C22, D10⋊C4.26C22, C23.23D1025C2, (C22×C20).383C22, (C22×C10).212C23, C55(C22.36C24), (C2×Dic5).248C23, (C4×Dic5).120C22, C10.D4.32C22, C2.23(Q8.10D10), (C2×Dic10).168C22, (C4×C5⋊D4)⋊59C2, C2.55(D5×C4○D4), C4⋊C4⋊D519C2, C4⋊C47D528C2, (C5×C22⋊Q8)⋊20C2, C10.167(C2×C4○D4), (C2×C4×D5).262C22, (C2×C4).54(C22×D5), (C5×C4⋊C4).165C22, (C2×C5⋊D4).139C22, (C5×C22⋊C4).39C22, SmallGroup(320,1312)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C10.552+ 1+4
C1C5C10C2×C10C22×D5C2×C4×D5D10⋊Q8 — C10.552+ 1+4
C5C2×C10 — C10.552+ 1+4
C1C22C22⋊Q8

Generators and relations for C10.552+ 1+4
 G = < a,b,c,d,e | a10=b4=e2=1, c2=a5, d2=a5b2, bab-1=dad-1=a-1, ac=ca, ae=ea, cbc-1=a5b-1, bd=db, ebe=a5b, cd=dc, ce=ec, ede=a5b2d >

Subgroups: 766 in 216 conjugacy classes, 93 normal (91 characteristic)
C1, C2 [×3], C2 [×3], C4 [×13], C22, C22 [×9], C5, C2×C4 [×6], C2×C4 [×10], D4 [×4], Q8 [×4], C23, C23 [×2], D5 [×2], C10 [×3], C10, C42 [×4], C22⋊C4 [×2], C22⋊C4 [×10], C4⋊C4 [×3], C4⋊C4 [×7], C22×C4, C22×C4 [×2], C2×D4 [×3], C2×Q8, C2×Q8 [×2], Dic5 [×2], Dic5 [×5], C20 [×6], D10 [×6], C2×C10, C2×C10 [×3], C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22⋊Q8 [×2], C22.D4 [×2], C4.4D4 [×3], C422C2 [×2], C4⋊Q8, Dic10 [×3], C4×D5 [×3], D20, C2×Dic5 [×6], C5⋊D4 [×3], C2×C20 [×6], C2×C20, C5×Q8, C22×D5 [×2], C22×C10, C22.36C24, C4×Dic5 [×4], C10.D4 [×6], C4⋊Dic5, D10⋊C4 [×8], C23.D5 [×2], C5×C22⋊C4 [×2], C5×C4⋊C4 [×3], C2×Dic10 [×2], C2×C4×D5 [×2], C2×D20, C2×C5⋊D4 [×2], C22×C20, Q8×C10, C23.D10, D10⋊D4, Dic5.5D4 [×2], Dic53Q8, C4⋊C47D5, D10.13D4, D10⋊Q8 [×2], C4⋊C4⋊D5, C4×C5⋊D4, C23.23D10, Dic5⋊Q8, C20.23D4, C5×C22⋊Q8, C10.552+ 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], C22.36C24, C23×D5, D46D10, Q8.10D10, D5×C4○D4, C10.552+ 1+4

Smallest permutation representation of C10.552+ 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 72 30 90)(2 71 21 89)(3 80 22 88)(4 79 23 87)(5 78 24 86)(6 77 25 85)(7 76 26 84)(8 75 27 83)(9 74 28 82)(10 73 29 81)(11 110 157 92)(12 109 158 91)(13 108 159 100)(14 107 160 99)(15 106 151 98)(16 105 152 97)(17 104 153 96)(18 103 154 95)(19 102 155 94)(20 101 156 93)(31 66 49 58)(32 65 50 57)(33 64 41 56)(34 63 42 55)(35 62 43 54)(36 61 44 53)(37 70 45 52)(38 69 46 51)(39 68 47 60)(40 67 48 59)(111 133 129 141)(112 132 130 150)(113 131 121 149)(114 140 122 148)(115 139 123 147)(116 138 124 146)(117 137 125 145)(118 136 126 144)(119 135 127 143)(120 134 128 142)
(1 97 6 92)(2 98 7 93)(3 99 8 94)(4 100 9 95)(5 91 10 96)(11 85 16 90)(12 86 17 81)(13 87 18 82)(14 88 19 83)(15 89 20 84)(21 106 26 101)(22 107 27 102)(23 108 28 103)(24 109 29 104)(25 110 30 105)(31 116 36 111)(32 117 37 112)(33 118 38 113)(34 119 39 114)(35 120 40 115)(41 126 46 121)(42 127 47 122)(43 128 48 123)(44 129 49 124)(45 130 50 125)(51 136 56 131)(52 137 57 132)(53 138 58 133)(54 139 59 134)(55 140 60 135)(61 146 66 141)(62 147 67 142)(63 148 68 143)(64 149 69 144)(65 150 70 145)(71 156 76 151)(72 157 77 152)(73 158 78 153)(74 159 79 154)(75 160 80 155)
(1 45 25 32)(2 44 26 31)(3 43 27 40)(4 42 28 39)(5 41 29 38)(6 50 30 37)(7 49 21 36)(8 48 22 35)(9 47 23 34)(10 46 24 33)(11 145 152 132)(12 144 153 131)(13 143 154 140)(14 142 155 139)(15 141 156 138)(16 150 157 137)(17 149 158 136)(18 148 159 135)(19 147 160 134)(20 146 151 133)(51 86 64 73)(52 85 65 72)(53 84 66 71)(54 83 67 80)(55 82 68 79)(56 81 69 78)(57 90 70 77)(58 89 61 76)(59 88 62 75)(60 87 63 74)(91 126 104 113)(92 125 105 112)(93 124 106 111)(94 123 107 120)(95 122 108 119)(96 121 109 118)(97 130 110 117)(98 129 101 116)(99 128 102 115)(100 127 103 114)
(1 32)(2 33)(3 34)(4 35)(5 36)(6 37)(7 38)(8 39)(9 40)(10 31)(11 137)(12 138)(13 139)(14 140)(15 131)(16 132)(17 133)(18 134)(19 135)(20 136)(21 41)(22 42)(23 43)(24 44)(25 45)(26 46)(27 47)(28 48)(29 49)(30 50)(51 89)(52 90)(53 81)(54 82)(55 83)(56 84)(57 85)(58 86)(59 87)(60 88)(61 73)(62 74)(63 75)(64 76)(65 77)(66 78)(67 79)(68 80)(69 71)(70 72)(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)(141 153)(142 154)(143 155)(144 156)(145 157)(146 158)(147 159)(148 160)(149 151)(150 152)

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

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

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

50 conjugacy classes

class 1 2A2B2C2D2E2F4A4B4C···4G4H4I4J4K4L4M4N4O5A5B10A···10F10G10H10I10J20A···20H20I···20P
order1222222444···4444444445510···101010101020···2020···20
size111142020224···41010101020202020222···244444···48···8

50 irreducible representations

dim1111111111111122222244444
type++++++++++++++++++++-
imageC1C2C2C2C2C2C2C2C2C2C2C2C2C2D5C4○D4D10D10D10D102+ 1+42- 1+4D46D10Q8.10D10D5×C4○D4
kernelC10.552+ 1+4C23.D10D10⋊D4Dic5.5D4Dic53Q8C4⋊C47D5D10.13D4D10⋊Q8C4⋊C4⋊D5C4×C5⋊D4C23.23D10Dic5⋊Q8C20.23D4C5×C22⋊Q8C22⋊Q8Dic5C22⋊C4C4⋊C4C22×C4C2×Q8C10C10C2C2C2
# reps1112111211111124462211444

Matrix representation of C10.552+ 1+4 in GL6(𝔽41)

4000000
0400000
00343400
007100
00003434
000071
,
3370000
23380000
00001740
0000324
0024100
00381700
,
900000
090000
00270340
00027034
00340140
00034014
,
4000000
0400000
00174000
0032400
00001740
0000324
,
4000000
1910000
00174000
0012400
00001740
0000124

G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,34,7,0,0,0,0,34,1,0,0,0,0,0,0,34,7,0,0,0,0,34,1],[3,23,0,0,0,0,37,38,0,0,0,0,0,0,0,0,24,38,0,0,0,0,1,17,0,0,17,3,0,0,0,0,40,24,0,0],[9,0,0,0,0,0,0,9,0,0,0,0,0,0,27,0,34,0,0,0,0,27,0,34,0,0,34,0,14,0,0,0,0,34,0,14],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,17,3,0,0,0,0,40,24,0,0,0,0,0,0,17,3,0,0,0,0,40,24],[40,19,0,0,0,0,0,1,0,0,0,0,0,0,17,1,0,0,0,0,40,24,0,0,0,0,0,0,17,1,0,0,0,0,40,24] >;

C10.552+ 1+4 in GAP, Magma, Sage, TeX

C_{10}._{55}2_+^{1+4}
% in TeX

G:=Group("C10.55ES+(2,2)");
// GroupNames label

G:=SmallGroup(320,1312);
// by ID

G=gap.SmallGroup(320,1312);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,120,758,555,100,1571,297,12550]);
// Polycyclic

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