metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.42- 1+4, C10.92+ 1+4, (C2×C4)⋊4D20, (C2×C20)⋊9D4, C4⋊D20⋊9C2, C20⋊7D4⋊5C2, C4.69(C2×D20), C4⋊C4.263D10, D10⋊2Q8⋊8C2, C20.222(C2×D4), C22.7(C2×D20), (C2×C10).54C24, C10.11(C22×D4), C2.13(C22×D20), (C2×C20).137C23, (C22×C4).179D10, C4⋊Dic5.29C22, C2.12(D4⋊6D10), C22.88(C23×D5), D10⋊C4.1C22, (C2×D20).262C22, (C22×C20).75C22, (C2×Dic5).16C23, (C22×D5).13C23, C23.226(C22×D5), (C22×C10).403C23, C2.7(Q8.10D10), C5⋊1(C22.31C24), (C2×Dic10).290C22, (C2×C4⋊C4)⋊19D5, (C10×C4⋊C4)⋊16C2, (C2×C4○D20)⋊16C2, (C2×C4×D5).64C22, (C2×C10).176(C2×D4), (C5×C4⋊C4).296C22, (C2×C4).572(C22×D5), (C2×C5⋊D4).101C22, SmallGroup(320,1182)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.2+ 1+4
G = < a,b,c,d,e | a10=b4=e2=1, c2=a5, d2=b2, bab-1=dad-1=eae=a-1, ac=ca, cbc-1=a5b-1, dbd-1=a5b, be=eb, dcd-1=ece=a5c, ede=a5b2d >
Subgroups: 1182 in 294 conjugacy classes, 111 normal (17 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C5, C2×C4, C2×C4, D4, Q8, C23, C23, D5, C10, C10, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic5, C20, C20, D10, C2×C10, C2×C10, C2×C10, C2×C4⋊C4, C4⋊D4, C22⋊Q8, C2×C4○D4, Dic10, C4×D5, D20, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C22×D5, C22×C10, C22.31C24, C4⋊Dic5, D10⋊C4, C5×C4⋊C4, C2×Dic10, C2×C4×D5, C2×D20, C4○D20, C2×C5⋊D4, C22×C20, C22×C20, C4⋊D20, D10⋊2Q8, C20⋊7D4, C10×C4⋊C4, C2×C4○D20, C10.2+ 1+4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C24, D10, C22×D4, 2+ 1+4, 2- 1+4, D20, C22×D5, C22.31C24, C2×D20, C23×D5, C22×D20, D4⋊6D10, Q8.10D10, C10.2+ 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 70 30 54)(2 69 21 53)(3 68 22 52)(4 67 23 51)(5 66 24 60)(6 65 25 59)(7 64 26 58)(8 63 27 57)(9 62 28 56)(10 61 29 55)(11 130 159 114)(12 129 160 113)(13 128 151 112)(14 127 152 111)(15 126 153 120)(16 125 154 119)(17 124 155 118)(18 123 156 117)(19 122 157 116)(20 121 158 115)(31 72 47 88)(32 71 48 87)(33 80 49 86)(34 79 50 85)(35 78 41 84)(36 77 42 83)(37 76 43 82)(38 75 44 81)(39 74 45 90)(40 73 46 89)(91 137 107 143)(92 136 108 142)(93 135 109 141)(94 134 110 150)(95 133 101 149)(96 132 102 148)(97 131 103 147)(98 140 104 146)(99 139 105 145)(100 138 106 144)
(1 39 6 34)(2 40 7 35)(3 31 8 36)(4 32 9 37)(5 33 10 38)(11 139 16 134)(12 140 17 135)(13 131 18 136)(14 132 19 137)(15 133 20 138)(21 46 26 41)(22 47 27 42)(23 48 28 43)(24 49 29 44)(25 50 30 45)(51 76 56 71)(52 77 57 72)(53 78 58 73)(54 79 59 74)(55 80 60 75)(61 86 66 81)(62 87 67 82)(63 88 68 83)(64 89 69 84)(65 90 70 85)(91 122 96 127)(92 123 97 128)(93 124 98 129)(94 125 99 130)(95 126 100 121)(101 120 106 115)(102 111 107 116)(103 112 108 117)(104 113 109 118)(105 114 110 119)(141 160 146 155)(142 151 147 156)(143 152 148 157)(144 153 149 158)(145 154 150 159)
(1 16 30 154)(2 15 21 153)(3 14 22 152)(4 13 23 151)(5 12 24 160)(6 11 25 159)(7 20 26 158)(8 19 27 157)(9 18 28 156)(10 17 29 155)(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)(51 117 67 123)(52 116 68 122)(53 115 69 121)(54 114 70 130)(55 113 61 129)(56 112 62 128)(57 111 63 127)(58 120 64 126)(59 119 65 125)(60 118 66 124)(71 103 87 97)(72 102 88 96)(73 101 89 95)(74 110 90 94)(75 109 81 93)(76 108 82 92)(77 107 83 91)(78 106 84 100)(79 105 85 99)(80 104 86 98)
(1 110)(2 109)(3 108)(4 107)(5 106)(6 105)(7 104)(8 103)(9 102)(10 101)(11 74)(12 73)(13 72)(14 71)(15 80)(16 79)(17 78)(18 77)(19 76)(20 75)(21 93)(22 92)(23 91)(24 100)(25 99)(26 98)(27 97)(28 96)(29 95)(30 94)(31 112)(32 111)(33 120)(34 119)(35 118)(36 117)(37 116)(38 115)(39 114)(40 113)(41 124)(42 123)(43 122)(44 121)(45 130)(46 129)(47 128)(48 127)(49 126)(50 125)(51 137)(52 136)(53 135)(54 134)(55 133)(56 132)(57 131)(58 140)(59 139)(60 138)(61 149)(62 148)(63 147)(64 146)(65 145)(66 144)(67 143)(68 142)(69 141)(70 150)(81 158)(82 157)(83 156)(84 155)(85 154)(86 153)(87 152)(88 151)(89 160)(90 159)
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), (1,70,30,54)(2,69,21,53)(3,68,22,52)(4,67,23,51)(5,66,24,60)(6,65,25,59)(7,64,26,58)(8,63,27,57)(9,62,28,56)(10,61,29,55)(11,130,159,114)(12,129,160,113)(13,128,151,112)(14,127,152,111)(15,126,153,120)(16,125,154,119)(17,124,155,118)(18,123,156,117)(19,122,157,116)(20,121,158,115)(31,72,47,88)(32,71,48,87)(33,80,49,86)(34,79,50,85)(35,78,41,84)(36,77,42,83)(37,76,43,82)(38,75,44,81)(39,74,45,90)(40,73,46,89)(91,137,107,143)(92,136,108,142)(93,135,109,141)(94,134,110,150)(95,133,101,149)(96,132,102,148)(97,131,103,147)(98,140,104,146)(99,139,105,145)(100,138,106,144), (1,39,6,34)(2,40,7,35)(3,31,8,36)(4,32,9,37)(5,33,10,38)(11,139,16,134)(12,140,17,135)(13,131,18,136)(14,132,19,137)(15,133,20,138)(21,46,26,41)(22,47,27,42)(23,48,28,43)(24,49,29,44)(25,50,30,45)(51,76,56,71)(52,77,57,72)(53,78,58,73)(54,79,59,74)(55,80,60,75)(61,86,66,81)(62,87,67,82)(63,88,68,83)(64,89,69,84)(65,90,70,85)(91,122,96,127)(92,123,97,128)(93,124,98,129)(94,125,99,130)(95,126,100,121)(101,120,106,115)(102,111,107,116)(103,112,108,117)(104,113,109,118)(105,114,110,119)(141,160,146,155)(142,151,147,156)(143,152,148,157)(144,153,149,158)(145,154,150,159), (1,16,30,154)(2,15,21,153)(3,14,22,152)(4,13,23,151)(5,12,24,160)(6,11,25,159)(7,20,26,158)(8,19,27,157)(9,18,28,156)(10,17,29,155)(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)(51,117,67,123)(52,116,68,122)(53,115,69,121)(54,114,70,130)(55,113,61,129)(56,112,62,128)(57,111,63,127)(58,120,64,126)(59,119,65,125)(60,118,66,124)(71,103,87,97)(72,102,88,96)(73,101,89,95)(74,110,90,94)(75,109,81,93)(76,108,82,92)(77,107,83,91)(78,106,84,100)(79,105,85,99)(80,104,86,98), (1,110)(2,109)(3,108)(4,107)(5,106)(6,105)(7,104)(8,103)(9,102)(10,101)(11,74)(12,73)(13,72)(14,71)(15,80)(16,79)(17,78)(18,77)(19,76)(20,75)(21,93)(22,92)(23,91)(24,100)(25,99)(26,98)(27,97)(28,96)(29,95)(30,94)(31,112)(32,111)(33,120)(34,119)(35,118)(36,117)(37,116)(38,115)(39,114)(40,113)(41,124)(42,123)(43,122)(44,121)(45,130)(46,129)(47,128)(48,127)(49,126)(50,125)(51,137)(52,136)(53,135)(54,134)(55,133)(56,132)(57,131)(58,140)(59,139)(60,138)(61,149)(62,148)(63,147)(64,146)(65,145)(66,144)(67,143)(68,142)(69,141)(70,150)(81,158)(82,157)(83,156)(84,155)(85,154)(86,153)(87,152)(88,151)(89,160)(90,159)>;
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), (1,70,30,54)(2,69,21,53)(3,68,22,52)(4,67,23,51)(5,66,24,60)(6,65,25,59)(7,64,26,58)(8,63,27,57)(9,62,28,56)(10,61,29,55)(11,130,159,114)(12,129,160,113)(13,128,151,112)(14,127,152,111)(15,126,153,120)(16,125,154,119)(17,124,155,118)(18,123,156,117)(19,122,157,116)(20,121,158,115)(31,72,47,88)(32,71,48,87)(33,80,49,86)(34,79,50,85)(35,78,41,84)(36,77,42,83)(37,76,43,82)(38,75,44,81)(39,74,45,90)(40,73,46,89)(91,137,107,143)(92,136,108,142)(93,135,109,141)(94,134,110,150)(95,133,101,149)(96,132,102,148)(97,131,103,147)(98,140,104,146)(99,139,105,145)(100,138,106,144), (1,39,6,34)(2,40,7,35)(3,31,8,36)(4,32,9,37)(5,33,10,38)(11,139,16,134)(12,140,17,135)(13,131,18,136)(14,132,19,137)(15,133,20,138)(21,46,26,41)(22,47,27,42)(23,48,28,43)(24,49,29,44)(25,50,30,45)(51,76,56,71)(52,77,57,72)(53,78,58,73)(54,79,59,74)(55,80,60,75)(61,86,66,81)(62,87,67,82)(63,88,68,83)(64,89,69,84)(65,90,70,85)(91,122,96,127)(92,123,97,128)(93,124,98,129)(94,125,99,130)(95,126,100,121)(101,120,106,115)(102,111,107,116)(103,112,108,117)(104,113,109,118)(105,114,110,119)(141,160,146,155)(142,151,147,156)(143,152,148,157)(144,153,149,158)(145,154,150,159), (1,16,30,154)(2,15,21,153)(3,14,22,152)(4,13,23,151)(5,12,24,160)(6,11,25,159)(7,20,26,158)(8,19,27,157)(9,18,28,156)(10,17,29,155)(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)(51,117,67,123)(52,116,68,122)(53,115,69,121)(54,114,70,130)(55,113,61,129)(56,112,62,128)(57,111,63,127)(58,120,64,126)(59,119,65,125)(60,118,66,124)(71,103,87,97)(72,102,88,96)(73,101,89,95)(74,110,90,94)(75,109,81,93)(76,108,82,92)(77,107,83,91)(78,106,84,100)(79,105,85,99)(80,104,86,98), (1,110)(2,109)(3,108)(4,107)(5,106)(6,105)(7,104)(8,103)(9,102)(10,101)(11,74)(12,73)(13,72)(14,71)(15,80)(16,79)(17,78)(18,77)(19,76)(20,75)(21,93)(22,92)(23,91)(24,100)(25,99)(26,98)(27,97)(28,96)(29,95)(30,94)(31,112)(32,111)(33,120)(34,119)(35,118)(36,117)(37,116)(38,115)(39,114)(40,113)(41,124)(42,123)(43,122)(44,121)(45,130)(46,129)(47,128)(48,127)(49,126)(50,125)(51,137)(52,136)(53,135)(54,134)(55,133)(56,132)(57,131)(58,140)(59,139)(60,138)(61,149)(62,148)(63,147)(64,146)(65,145)(66,144)(67,143)(68,142)(69,141)(70,150)(81,158)(82,157)(83,156)(84,155)(85,154)(86,153)(87,152)(88,151)(89,160)(90,159) );
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)], [(1,70,30,54),(2,69,21,53),(3,68,22,52),(4,67,23,51),(5,66,24,60),(6,65,25,59),(7,64,26,58),(8,63,27,57),(9,62,28,56),(10,61,29,55),(11,130,159,114),(12,129,160,113),(13,128,151,112),(14,127,152,111),(15,126,153,120),(16,125,154,119),(17,124,155,118),(18,123,156,117),(19,122,157,116),(20,121,158,115),(31,72,47,88),(32,71,48,87),(33,80,49,86),(34,79,50,85),(35,78,41,84),(36,77,42,83),(37,76,43,82),(38,75,44,81),(39,74,45,90),(40,73,46,89),(91,137,107,143),(92,136,108,142),(93,135,109,141),(94,134,110,150),(95,133,101,149),(96,132,102,148),(97,131,103,147),(98,140,104,146),(99,139,105,145),(100,138,106,144)], [(1,39,6,34),(2,40,7,35),(3,31,8,36),(4,32,9,37),(5,33,10,38),(11,139,16,134),(12,140,17,135),(13,131,18,136),(14,132,19,137),(15,133,20,138),(21,46,26,41),(22,47,27,42),(23,48,28,43),(24,49,29,44),(25,50,30,45),(51,76,56,71),(52,77,57,72),(53,78,58,73),(54,79,59,74),(55,80,60,75),(61,86,66,81),(62,87,67,82),(63,88,68,83),(64,89,69,84),(65,90,70,85),(91,122,96,127),(92,123,97,128),(93,124,98,129),(94,125,99,130),(95,126,100,121),(101,120,106,115),(102,111,107,116),(103,112,108,117),(104,113,109,118),(105,114,110,119),(141,160,146,155),(142,151,147,156),(143,152,148,157),(144,153,149,158),(145,154,150,159)], [(1,16,30,154),(2,15,21,153),(3,14,22,152),(4,13,23,151),(5,12,24,160),(6,11,25,159),(7,20,26,158),(8,19,27,157),(9,18,28,156),(10,17,29,155),(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),(51,117,67,123),(52,116,68,122),(53,115,69,121),(54,114,70,130),(55,113,61,129),(56,112,62,128),(57,111,63,127),(58,120,64,126),(59,119,65,125),(60,118,66,124),(71,103,87,97),(72,102,88,96),(73,101,89,95),(74,110,90,94),(75,109,81,93),(76,108,82,92),(77,107,83,91),(78,106,84,100),(79,105,85,99),(80,104,86,98)], [(1,110),(2,109),(3,108),(4,107),(5,106),(6,105),(7,104),(8,103),(9,102),(10,101),(11,74),(12,73),(13,72),(14,71),(15,80),(16,79),(17,78),(18,77),(19,76),(20,75),(21,93),(22,92),(23,91),(24,100),(25,99),(26,98),(27,97),(28,96),(29,95),(30,94),(31,112),(32,111),(33,120),(34,119),(35,118),(36,117),(37,116),(38,115),(39,114),(40,113),(41,124),(42,123),(43,122),(44,121),(45,130),(46,129),(47,128),(48,127),(49,126),(50,125),(51,137),(52,136),(53,135),(54,134),(55,133),(56,132),(57,131),(58,140),(59,139),(60,138),(61,149),(62,148),(63,147),(64,146),(65,145),(66,144),(67,143),(68,142),(69,141),(70,150),(81,158),(82,157),(83,156),(84,155),(85,154),(86,153),(87,152),(88,151),(89,160),(90,159)]])
62 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 5A | 5B | 10A | ··· | 10N | 20A | ··· | 20X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
62 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D5 | D10 | D10 | D20 | 2+ 1+4 | 2- 1+4 | D4⋊6D10 | Q8.10D10 |
| kernel | C10.2+ 1+4 | C4⋊D20 | D10⋊2Q8 | C20⋊7D4 | C10×C4⋊C4 | C2×C4○D20 | C2×C20 | C2×C4⋊C4 | C4⋊C4 | C22×C4 | C2×C4 | C10 | C10 | C2 | C2 |
| # reps | 1 | 4 | 4 | 4 | 1 | 2 | 4 | 2 | 8 | 6 | 16 | 1 | 1 | 4 | 4 |
Matrix representation of C10.2+ 1+4 ►in GL6(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 35 | 34 | 0 | 0 |
| 0 | 0 | 6 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 35 | 34 |
| 0 | 0 | 0 | 0 | 6 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 8 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 38 | 0 | 0 |
| 0 | 0 | 38 | 20 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 38 |
| 0 | 0 | 0 | 0 | 38 | 20 |
| 20 | 36 | 0 | 0 | 0 | 0 |
| 31 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 20 | 36 | 0 | 0 | 0 | 0 |
| 6 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 24 | 18 | 21 |
| 0 | 0 | 18 | 38 | 26 | 23 |
| 0 | 0 | 18 | 21 | 38 | 17 |
| 0 | 0 | 26 | 23 | 23 | 3 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 8 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 32 | 10 | 22 |
| 0 | 0 | 32 | 19 | 22 | 31 |
| 0 | 0 | 10 | 22 | 19 | 9 |
| 0 | 0 | 22 | 31 | 9 | 22 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,35,6,0,0,0,0,34,0,0,0,0,0,0,0,35,6,0,0,0,0,34,0],[1,8,0,0,0,0,0,40,0,0,0,0,0,0,21,38,0,0,0,0,38,20,0,0,0,0,0,0,21,38,0,0,0,0,38,20],[20,31,0,0,0,0,36,21,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,1,0,0,0,0,0,0,1,0,0],[20,6,0,0,0,0,36,21,0,0,0,0,0,0,3,18,18,26,0,0,24,38,21,23,0,0,18,26,38,23,0,0,21,23,17,3],[1,8,0,0,0,0,0,40,0,0,0,0,0,0,22,32,10,22,0,0,32,19,22,31,0,0,10,22,19,9,0,0,22,31,9,22] >;
C10.2+ 1+4 in GAP, Magma, Sage, TeX
C_{10}.2_+^{1+4} % in TeX
G:=Group("C10.ES+(2,2)"); // GroupNames label
G:=SmallGroup(320,1182);
// by ID
G=gap.SmallGroup(320,1182);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,758,675,570,80,12550]);
// 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=d*a*d^-1=e*a*e=a^-1,a*c=c*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