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G = C10.392+ 1+4order 320 = 26·5

39th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C10.392+ 1+4, C10.722- 1+4, (C4×D5)⋊2D4, C4⋊D411D5, C4.184(D4×D5), C202D419C2, C4⋊C4.180D10, (C2×D4).92D10, D10.15(C2×D4), C20.228(C2×D4), C22⋊C4.8D10, D10⋊D419C2, D102Q821C2, (C2×C20).39C23, Dic5.86(C2×D4), C10.67(C22×D4), Dic5⋊D413C2, C20.48D434C2, (C2×C10).152C24, (C22×C4).223D10, C2.41(D46D10), C23.16(C22×D5), (C2×D20).228C22, (D4×C10).122C22, C4⋊Dic5.207C22, (C2×Dic5).73C23, C22.173(C23×D5), Dic5.14D419C2, C23.D5.25C22, D10⋊C4.15C22, (C22×C10).187C23, (C22×C20).241C22, C53(C22.31C24), C10.D4.18C22, (C22×D5).197C23, C2.30(D4.10D10), (C2×Dic10).160C22, (C22×Dic5).109C22, C2.40(C2×D4×D5), (D5×C4⋊C4)⋊21C2, (C2×C4○D20)⋊21C2, (C5×C4⋊D4)⋊14C2, (C2×D42D5)⋊13C2, (C2×C4×D5).92C22, (C5×C4⋊C4).144C22, (C2×C4).586(C22×D5), (C2×C5⋊D4).28C22, (C5×C22⋊C4).13C22, SmallGroup(320,1280)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C10.392+ 1+4
C1C5C10C2×C10C22×D5C2×C4×D5C2×C4○D20 — C10.392+ 1+4
C5C2×C10 — C10.392+ 1+4
C1C22C4⋊D4

Generators and relations for C10.392+ 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=a5b-1, dbd-1=a5b, be=eb, dcd-1=ece=a5c, ede=a5b2d >

Subgroups: 1102 in 294 conjugacy classes, 103 normal (43 characteristic)
C1, C2 [×3], C2 [×6], C4 [×2], C4 [×10], C22, C22 [×16], C5, C2×C4 [×2], C2×C4 [×2], C2×C4 [×20], D4 [×16], Q8 [×4], C23, C23 [×2], C23 [×2], D5 [×3], C10 [×3], C10 [×3], C22⋊C4 [×2], C22⋊C4 [×6], C4⋊C4, C4⋊C4 [×7], C22×C4, C22×C4 [×6], C2×D4, C2×D4 [×2], C2×D4 [×7], C2×Q8 [×2], C4○D4 [×8], Dic5 [×2], Dic5 [×5], C20 [×2], C20 [×3], D10 [×2], D10 [×5], C2×C10, C2×C10 [×9], C2×C4⋊C4, C4⋊D4, C4⋊D4 [×7], C22⋊Q8 [×4], C2×C4○D4 [×2], Dic10 [×4], C4×D5 [×4], C4×D5 [×4], D20 [×2], C2×Dic5 [×2], C2×Dic5 [×4], C2×Dic5 [×4], C5⋊D4 [×10], C2×C20 [×2], C2×C20 [×2], C2×C20 [×2], C5×D4 [×4], C22×D5 [×2], C22×C10, C22×C10 [×2], C22.31C24, C10.D4 [×4], C4⋊Dic5, C4⋊Dic5 [×2], D10⋊C4 [×2], C23.D5 [×4], C5×C22⋊C4 [×2], C5×C4⋊C4, C2×Dic10 [×2], C2×C4×D5 [×2], C2×C4×D5 [×2], C2×D20, C4○D20 [×4], D42D5 [×4], C22×Dic5 [×2], C2×C5⋊D4 [×2], C2×C5⋊D4 [×4], C22×C20, D4×C10, D4×C10 [×2], Dic5.14D4 [×2], D10⋊D4 [×2], D5×C4⋊C4, D102Q8, C20.48D4, C202D4, C202D4 [×2], Dic5⋊D4 [×2], C5×C4⋊D4, C2×C4○D20, C2×D42D5, C10.392+ 1+4
Quotients: C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D5, C2×D4 [×6], C24, D10 [×7], C22×D4, 2+ 1+4, 2- 1+4, C22×D5 [×7], C22.31C24, D4×D5 [×2], C23×D5, C2×D4×D5, D46D10, D4.10D10, C10.392+ 1+4

Smallest permutation representation of C10.392+ 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 90 30 78)(2 89 21 77)(3 88 22 76)(4 87 23 75)(5 86 24 74)(6 85 25 73)(7 84 26 72)(8 83 27 71)(9 82 28 80)(10 81 29 79)(11 93 153 105)(12 92 154 104)(13 91 155 103)(14 100 156 102)(15 99 157 101)(16 98 158 110)(17 97 159 109)(18 96 160 108)(19 95 151 107)(20 94 152 106)(31 62 43 60)(32 61 44 59)(33 70 45 58)(34 69 46 57)(35 68 47 56)(36 67 48 55)(37 66 49 54)(38 65 50 53)(39 64 41 52)(40 63 42 51)(111 140 123 142)(112 139 124 141)(113 138 125 150)(114 137 126 149)(115 136 127 148)(116 135 128 147)(117 134 129 146)(118 133 130 145)(119 132 121 144)(120 131 122 143)
(1 45 6 50)(2 44 7 49)(3 43 8 48)(4 42 9 47)(5 41 10 46)(11 138 16 133)(12 137 17 132)(13 136 18 131)(14 135 19 140)(15 134 20 139)(21 32 26 37)(22 31 27 36)(23 40 28 35)(24 39 29 34)(25 38 30 33)(51 75 56 80)(52 74 57 79)(53 73 58 78)(54 72 59 77)(55 71 60 76)(61 89 66 84)(62 88 67 83)(63 87 68 82)(64 86 69 81)(65 85 70 90)(91 120 96 115)(92 119 97 114)(93 118 98 113)(94 117 99 112)(95 116 100 111)(101 124 106 129)(102 123 107 128)(103 122 108 127)(104 121 109 126)(105 130 110 125)(141 157 146 152)(142 156 147 151)(143 155 148 160)(144 154 149 159)(145 153 150 158)
(1 150 30 138)(2 141 21 139)(3 142 22 140)(4 143 23 131)(5 144 24 132)(6 145 25 133)(7 146 26 134)(8 147 27 135)(9 148 28 136)(10 149 29 137)(11 45 153 33)(12 46 154 34)(13 47 155 35)(14 48 156 36)(15 49 157 37)(16 50 158 38)(17 41 159 39)(18 42 160 40)(19 43 151 31)(20 44 152 32)(51 103 63 91)(52 104 64 92)(53 105 65 93)(54 106 66 94)(55 107 67 95)(56 108 68 96)(57 109 69 97)(58 110 70 98)(59 101 61 99)(60 102 62 100)(71 123 83 111)(72 124 84 112)(73 125 85 113)(74 126 86 114)(75 127 87 115)(76 128 88 116)(77 129 89 117)(78 130 90 118)(79 121 81 119)(80 122 82 120)
(1 33)(2 34)(3 35)(4 36)(5 37)(6 38)(7 39)(8 40)(9 31)(10 32)(11 133)(12 134)(13 135)(14 136)(15 137)(16 138)(17 139)(18 140)(19 131)(20 132)(21 46)(22 47)(23 48)(24 49)(25 50)(26 41)(27 42)(28 43)(29 44)(30 45)(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)(91 128)(92 129)(93 130)(94 121)(95 122)(96 123)(97 124)(98 125)(99 126)(100 127)(101 114)(102 115)(103 116)(104 117)(105 118)(106 119)(107 120)(108 111)(109 112)(110 113)(141 159)(142 160)(143 151)(144 152)(145 153)(146 154)(147 155)(148 156)(149 157)(150 158)

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

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

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

50 conjugacy classes

class 1 2A2B2C2D2E2F2G2H2I4A4B4C4D4E4F4G4H···4L5A5B10A···10F10G10H10I10J10K10L10M10N20A···20H20I20J20K20L
order122222222244444444···45510···10101010101010101020···2020202020
size111144410102022444101020···20222···2444488884···48888

50 irreducible representations

dim1111111111122222244444
type++++++++++++++++++-+-
imageC1C2C2C2C2C2C2C2C2C2C2D4D5D10D10D10D102+ 1+42- 1+4D4×D5D46D10D4.10D10
kernelC10.392+ 1+4Dic5.14D4D10⋊D4D5×C4⋊C4D102Q8C20.48D4C202D4Dic5⋊D4C5×C4⋊D4C2×C4○D20C2×D42D5C4×D5C4⋊D4C22⋊C4C4⋊C4C22×C4C2×D4C10C10C4C2C2
# reps1221113211142422611444

Matrix representation of C10.392+ 1+4 in GL8(𝔽41)

77000000
3440000000
004000000
000400000
000040000
000004000
000000400
000000040
,
400000000
71000000
00010000
00100000
000010039
0000400401
00000101
000010040
,
10000000
3440000000
000400000
00100000
00001200
0000404000
0000040040
00001110
,
400000000
040000000
004000000
00010000
0000183510
00002032021
000003203
00002118240
,
10000000
01000000
00010000
00100000
00001200
000004000
0000404001
00001110

G:=sub<GL(8,GF(41))| [7,34,0,0,0,0,0,0,7,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40],[40,7,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,40,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,39,1,1,40],[1,34,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,1,40,0,1,0,0,0,0,2,40,40,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0],[40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,18,20,0,21,0,0,0,0,35,3,3,18,0,0,0,0,1,20,20,24,0,0,0,0,0,21,3,0],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,40,1,0,0,0,0,2,40,40,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;

C10.392+ 1+4 in GAP, Magma, Sage, TeX

C_{10}._{39}2_+^{1+4}
% in TeX

G:=Group("C10.39ES+(2,2)");
// GroupNames label

G:=SmallGroup(320,1280);
// by ID

G=gap.SmallGroup(320,1280);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,758,1123,570,185,12550]);
// 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=a^5*b^-1,d*b*d^-1=a^5*b,b*e=e*b,d*c*d^-1=e*c*e=a^5*c,e*d*e=a^5*b^2*d>;
// generators/relations

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