metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.322+ 1+4, C10.682- 1+4, C4⋊D4⋊5D5, C4⋊C4.89D10, (C2×Dic5)⋊9D4, C20⋊7D4⋊43C2, C22.2(D4×D5), (C2×D4).89D10, C22⋊C4.4D10, D10⋊D4⋊16C2, D10⋊Q8⋊13C2, Dic5⋊D4⋊8C2, Dic5.85(C2×D4), C10.60(C22×D4), C23.8(C22×D5), (C2×C20).172C23, (C2×C10).141C24, (C2×D20).32C22, (C22×C4).217D10, C4⋊Dic5.44C22, C2.34(D4⋊6D10), (D4×C10).115C22, (C22×C10).12C23, (C22×D5).60C23, C22.162(C23×D5), Dic5.14D4⋊15C2, C23.D5.19C22, D10⋊C4.69C22, (C22×C20).310C22, C5⋊2(C22.31C24), (C2×Dic5).234C23, C2.26(D4.10D10), (C2×Dic10).157C22, C10.D4.158C22, (C22×Dic5).102C22, C2.33(C2×D4×D5), (C5×C4⋊D4)⋊6C2, (C2×C10).4(C2×D4), (C2×D4⋊2D5)⋊9C2, (C2×C4×D5).89C22, (C2×C4).35(C22×D5), (C2×C10.D4)⋊28C2, (C5×C4⋊C4).137C22, (C2×C5⋊D4).24C22, (C5×C22⋊C4).6C22, SmallGroup(320,1269)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.322+ 1+4
G = < a,b,c,d,e | a10=b4=e2=1, c2=a5, d2=b2, ab=ba, cac-1=eae=a-1, ad=da, cbc-1=a5b-1, dbd-1=a5b, be=eb, dcd-1=ece=a5c, ede=a5b2d >
Subgroups: 1102 in 294 conjugacy classes, 103 normal (31 characteristic)
C1, C2 [×3], C2 [×6], C4 [×12], C22, C22 [×2], C22 [×14], C5, C2×C4 [×2], C2×C4 [×2], C2×C4 [×20], D4 [×16], Q8 [×4], C23, C23 [×2], C23 [×2], D5 [×2], C10 [×3], C10 [×4], 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 [×4], Dic5 [×4], C20 [×4], D10 [×6], C2×C10, C2×C10 [×2], C2×C10 [×8], C2×C4⋊C4, C4⋊D4, C4⋊D4 [×7], C22⋊Q8 [×4], C2×C4○D4 [×2], Dic10 [×4], C4×D5 [×4], D20, C2×Dic5 [×10], C2×Dic5 [×5], C5⋊D4 [×10], C2×C20 [×2], C2×C20 [×2], C2×C20, C5×D4 [×5], C22×D5 [×2], C22×C10, C22×C10 [×2], C22.31C24, C10.D4 [×6], C4⋊Dic5, D10⋊C4 [×4], C23.D5 [×2], C5×C22⋊C4 [×2], C5×C4⋊C4, C2×Dic10 [×2], C2×C4×D5 [×2], C2×D20, D4⋊2D5 [×8], C22×Dic5 [×2], C22×Dic5 [×2], C2×C5⋊D4 [×6], C22×C20, D4×C10, D4×C10 [×2], Dic5.14D4 [×2], D10⋊D4 [×2], D10⋊Q8 [×2], C2×C10.D4, C20⋊7D4, Dic5⋊D4 [×4], C5×C4⋊D4, C2×D4⋊2D5 [×2], C10.322+ 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, D4⋊6D10, D4.10D10, C10.322+ 1+4
(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)
(1 138 30 150)(2 139 21 141)(3 140 22 142)(4 131 23 143)(5 132 24 144)(6 133 25 145)(7 134 26 146)(8 135 27 147)(9 136 28 148)(10 137 29 149)(11 33 153 45)(12 34 154 46)(13 35 155 47)(14 36 156 48)(15 37 157 49)(16 38 158 50)(17 39 159 41)(18 40 160 42)(19 31 151 43)(20 32 152 44)(51 91 63 103)(52 92 64 104)(53 93 65 105)(54 94 66 106)(55 95 67 107)(56 96 68 108)(57 97 69 109)(58 98 70 110)(59 99 61 101)(60 100 62 102)(71 111 83 123)(72 112 84 124)(73 113 85 125)(74 114 86 126)(75 115 87 127)(76 116 88 128)(77 117 89 129)(78 118 90 130)(79 119 81 121)(80 120 82 122)
(1 45 6 50)(2 44 7 49)(3 43 8 48)(4 42 9 47)(5 41 10 46)(11 150 16 145)(12 149 17 144)(13 148 18 143)(14 147 19 142)(15 146 20 141)(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)(91 122 96 127)(92 121 97 126)(93 130 98 125)(94 129 99 124)(95 128 100 123)(101 112 106 117)(102 111 107 116)(103 120 108 115)(104 119 109 114)(105 118 110 113)(131 155 136 160)(132 154 137 159)(133 153 138 158)(134 152 139 157)(135 151 140 156)
(1 125 30 113)(2 126 21 114)(3 127 22 115)(4 128 23 116)(5 129 24 117)(6 130 25 118)(7 121 26 119)(8 122 27 120)(9 123 28 111)(10 124 29 112)(11 65 153 53)(12 66 154 54)(13 67 155 55)(14 68 156 56)(15 69 157 57)(16 70 158 58)(17 61 159 59)(18 62 160 60)(19 63 151 51)(20 64 152 52)(31 108 43 96)(32 109 44 97)(33 110 45 98)(34 101 46 99)(35 102 47 100)(36 103 48 91)(37 104 49 92)(38 105 50 93)(39 106 41 94)(40 107 42 95)(71 143 83 131)(72 144 84 132)(73 145 85 133)(74 146 86 134)(75 147 87 135)(76 148 88 136)(77 149 89 137)(78 150 90 138)(79 141 81 139)(80 142 82 140)
(1 30)(2 29)(3 28)(4 27)(5 26)(6 25)(7 24)(8 23)(9 22)(10 21)(11 158)(12 157)(13 156)(14 155)(15 154)(16 153)(17 152)(18 151)(19 160)(20 159)(31 42)(32 41)(33 50)(34 49)(35 48)(36 47)(37 46)(38 45)(39 44)(40 43)(51 55)(52 54)(56 60)(57 59)(61 69)(62 68)(63 67)(64 66)(71 80)(72 79)(73 78)(74 77)(75 76)(81 84)(82 83)(85 90)(86 89)(87 88)(91 95)(92 94)(96 100)(97 99)(101 109)(102 108)(103 107)(104 106)(111 120)(112 119)(113 118)(114 117)(115 116)(121 124)(122 123)(125 130)(126 129)(127 128)(131 147)(132 146)(133 145)(134 144)(135 143)(136 142)(137 141)(138 150)(139 149)(140 148)
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), (1,138,30,150)(2,139,21,141)(3,140,22,142)(4,131,23,143)(5,132,24,144)(6,133,25,145)(7,134,26,146)(8,135,27,147)(9,136,28,148)(10,137,29,149)(11,33,153,45)(12,34,154,46)(13,35,155,47)(14,36,156,48)(15,37,157,49)(16,38,158,50)(17,39,159,41)(18,40,160,42)(19,31,151,43)(20,32,152,44)(51,91,63,103)(52,92,64,104)(53,93,65,105)(54,94,66,106)(55,95,67,107)(56,96,68,108)(57,97,69,109)(58,98,70,110)(59,99,61,101)(60,100,62,102)(71,111,83,123)(72,112,84,124)(73,113,85,125)(74,114,86,126)(75,115,87,127)(76,116,88,128)(77,117,89,129)(78,118,90,130)(79,119,81,121)(80,120,82,122), (1,45,6,50)(2,44,7,49)(3,43,8,48)(4,42,9,47)(5,41,10,46)(11,150,16,145)(12,149,17,144)(13,148,18,143)(14,147,19,142)(15,146,20,141)(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)(91,122,96,127)(92,121,97,126)(93,130,98,125)(94,129,99,124)(95,128,100,123)(101,112,106,117)(102,111,107,116)(103,120,108,115)(104,119,109,114)(105,118,110,113)(131,155,136,160)(132,154,137,159)(133,153,138,158)(134,152,139,157)(135,151,140,156), (1,125,30,113)(2,126,21,114)(3,127,22,115)(4,128,23,116)(5,129,24,117)(6,130,25,118)(7,121,26,119)(8,122,27,120)(9,123,28,111)(10,124,29,112)(11,65,153,53)(12,66,154,54)(13,67,155,55)(14,68,156,56)(15,69,157,57)(16,70,158,58)(17,61,159,59)(18,62,160,60)(19,63,151,51)(20,64,152,52)(31,108,43,96)(32,109,44,97)(33,110,45,98)(34,101,46,99)(35,102,47,100)(36,103,48,91)(37,104,49,92)(38,105,50,93)(39,106,41,94)(40,107,42,95)(71,143,83,131)(72,144,84,132)(73,145,85,133)(74,146,86,134)(75,147,87,135)(76,148,88,136)(77,149,89,137)(78,150,90,138)(79,141,81,139)(80,142,82,140), (1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,158)(12,157)(13,156)(14,155)(15,154)(16,153)(17,152)(18,151)(19,160)(20,159)(31,42)(32,41)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(51,55)(52,54)(56,60)(57,59)(61,69)(62,68)(63,67)(64,66)(71,80)(72,79)(73,78)(74,77)(75,76)(81,84)(82,83)(85,90)(86,89)(87,88)(91,95)(92,94)(96,100)(97,99)(101,109)(102,108)(103,107)(104,106)(111,120)(112,119)(113,118)(114,117)(115,116)(121,124)(122,123)(125,130)(126,129)(127,128)(131,147)(132,146)(133,145)(134,144)(135,143)(136,142)(137,141)(138,150)(139,149)(140,148)>;
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), (1,138,30,150)(2,139,21,141)(3,140,22,142)(4,131,23,143)(5,132,24,144)(6,133,25,145)(7,134,26,146)(8,135,27,147)(9,136,28,148)(10,137,29,149)(11,33,153,45)(12,34,154,46)(13,35,155,47)(14,36,156,48)(15,37,157,49)(16,38,158,50)(17,39,159,41)(18,40,160,42)(19,31,151,43)(20,32,152,44)(51,91,63,103)(52,92,64,104)(53,93,65,105)(54,94,66,106)(55,95,67,107)(56,96,68,108)(57,97,69,109)(58,98,70,110)(59,99,61,101)(60,100,62,102)(71,111,83,123)(72,112,84,124)(73,113,85,125)(74,114,86,126)(75,115,87,127)(76,116,88,128)(77,117,89,129)(78,118,90,130)(79,119,81,121)(80,120,82,122), (1,45,6,50)(2,44,7,49)(3,43,8,48)(4,42,9,47)(5,41,10,46)(11,150,16,145)(12,149,17,144)(13,148,18,143)(14,147,19,142)(15,146,20,141)(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)(91,122,96,127)(92,121,97,126)(93,130,98,125)(94,129,99,124)(95,128,100,123)(101,112,106,117)(102,111,107,116)(103,120,108,115)(104,119,109,114)(105,118,110,113)(131,155,136,160)(132,154,137,159)(133,153,138,158)(134,152,139,157)(135,151,140,156), (1,125,30,113)(2,126,21,114)(3,127,22,115)(4,128,23,116)(5,129,24,117)(6,130,25,118)(7,121,26,119)(8,122,27,120)(9,123,28,111)(10,124,29,112)(11,65,153,53)(12,66,154,54)(13,67,155,55)(14,68,156,56)(15,69,157,57)(16,70,158,58)(17,61,159,59)(18,62,160,60)(19,63,151,51)(20,64,152,52)(31,108,43,96)(32,109,44,97)(33,110,45,98)(34,101,46,99)(35,102,47,100)(36,103,48,91)(37,104,49,92)(38,105,50,93)(39,106,41,94)(40,107,42,95)(71,143,83,131)(72,144,84,132)(73,145,85,133)(74,146,86,134)(75,147,87,135)(76,148,88,136)(77,149,89,137)(78,150,90,138)(79,141,81,139)(80,142,82,140), (1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,158)(12,157)(13,156)(14,155)(15,154)(16,153)(17,152)(18,151)(19,160)(20,159)(31,42)(32,41)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(51,55)(52,54)(56,60)(57,59)(61,69)(62,68)(63,67)(64,66)(71,80)(72,79)(73,78)(74,77)(75,76)(81,84)(82,83)(85,90)(86,89)(87,88)(91,95)(92,94)(96,100)(97,99)(101,109)(102,108)(103,107)(104,106)(111,120)(112,119)(113,118)(114,117)(115,116)(121,124)(122,123)(125,130)(126,129)(127,128)(131,147)(132,146)(133,145)(134,144)(135,143)(136,142)(137,141)(138,150)(139,149)(140,148) );
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)], [(1,138,30,150),(2,139,21,141),(3,140,22,142),(4,131,23,143),(5,132,24,144),(6,133,25,145),(7,134,26,146),(8,135,27,147),(9,136,28,148),(10,137,29,149),(11,33,153,45),(12,34,154,46),(13,35,155,47),(14,36,156,48),(15,37,157,49),(16,38,158,50),(17,39,159,41),(18,40,160,42),(19,31,151,43),(20,32,152,44),(51,91,63,103),(52,92,64,104),(53,93,65,105),(54,94,66,106),(55,95,67,107),(56,96,68,108),(57,97,69,109),(58,98,70,110),(59,99,61,101),(60,100,62,102),(71,111,83,123),(72,112,84,124),(73,113,85,125),(74,114,86,126),(75,115,87,127),(76,116,88,128),(77,117,89,129),(78,118,90,130),(79,119,81,121),(80,120,82,122)], [(1,45,6,50),(2,44,7,49),(3,43,8,48),(4,42,9,47),(5,41,10,46),(11,150,16,145),(12,149,17,144),(13,148,18,143),(14,147,19,142),(15,146,20,141),(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),(91,122,96,127),(92,121,97,126),(93,130,98,125),(94,129,99,124),(95,128,100,123),(101,112,106,117),(102,111,107,116),(103,120,108,115),(104,119,109,114),(105,118,110,113),(131,155,136,160),(132,154,137,159),(133,153,138,158),(134,152,139,157),(135,151,140,156)], [(1,125,30,113),(2,126,21,114),(3,127,22,115),(4,128,23,116),(5,129,24,117),(6,130,25,118),(7,121,26,119),(8,122,27,120),(9,123,28,111),(10,124,29,112),(11,65,153,53),(12,66,154,54),(13,67,155,55),(14,68,156,56),(15,69,157,57),(16,70,158,58),(17,61,159,59),(18,62,160,60),(19,63,151,51),(20,64,152,52),(31,108,43,96),(32,109,44,97),(33,110,45,98),(34,101,46,99),(35,102,47,100),(36,103,48,91),(37,104,49,92),(38,105,50,93),(39,106,41,94),(40,107,42,95),(71,143,83,131),(72,144,84,132),(73,145,85,133),(74,146,86,134),(75,147,87,135),(76,148,88,136),(77,149,89,137),(78,150,90,138),(79,141,81,139),(80,142,82,140)], [(1,30),(2,29),(3,28),(4,27),(5,26),(6,25),(7,24),(8,23),(9,22),(10,21),(11,158),(12,157),(13,156),(14,155),(15,154),(16,153),(17,152),(18,151),(19,160),(20,159),(31,42),(32,41),(33,50),(34,49),(35,48),(36,47),(37,46),(38,45),(39,44),(40,43),(51,55),(52,54),(56,60),(57,59),(61,69),(62,68),(63,67),(64,66),(71,80),(72,79),(73,78),(74,77),(75,76),(81,84),(82,83),(85,90),(86,89),(87,88),(91,95),(92,94),(96,100),(97,99),(101,109),(102,108),(103,107),(104,106),(111,120),(112,119),(113,118),(114,117),(115,116),(121,124),(122,123),(125,130),(126,129),(127,128),(131,147),(132,146),(133,145),(134,144),(135,143),(136,142),(137,141),(138,150),(139,149),(140,148)])
50 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 | ··· | 10F | 10G | 10H | 10I | 10J | 10K | 10L | 10M | 10N | 20A | ··· | 20H | 20I | 20J | 20K | 20L |
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 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | 20 | 20 | 20 |
size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 20 | 20 | 4 | 4 | 4 | 4 | 10 | 10 | 10 | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | 8 | 8 | 8 |
50 irreducible representations
dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | |
image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D5 | D10 | D10 | D10 | D10 | 2+ 1+4 | 2- 1+4 | D4×D5 | D4⋊6D10 | D4.10D10 |
kernel | C10.322+ 1+4 | Dic5.14D4 | D10⋊D4 | D10⋊Q8 | C2×C10.D4 | C20⋊7D4 | Dic5⋊D4 | C5×C4⋊D4 | C2×D4⋊2D5 | C2×Dic5 | C4⋊D4 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C10 | C10 | C22 | C2 | C2 |
# reps | 1 | 2 | 2 | 2 | 1 | 1 | 4 | 1 | 2 | 4 | 2 | 4 | 2 | 2 | 6 | 1 | 1 | 4 | 4 | 4 |
Matrix representation of C10.322+ 1+4 ►in GL6(𝔽41)
40 | 0 | 0 | 0 | 0 | 0 |
0 | 40 | 0 | 0 | 0 | 0 |
0 | 0 | 6 | 6 | 0 | 0 |
0 | 0 | 35 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 6 | 6 |
0 | 0 | 0 | 0 | 35 | 1 |
1 | 0 | 0 | 0 | 0 | 0 |
1 | 40 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 39 | 28 |
0 | 0 | 0 | 0 | 13 | 2 |
0 | 0 | 39 | 28 | 0 | 0 |
0 | 0 | 13 | 2 | 0 | 0 |
40 | 2 | 0 | 0 | 0 | 0 |
40 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 40 | 0 |
0 | 0 | 0 | 0 | 35 | 1 |
0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 6 | 40 | 0 | 0 |
40 | 2 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 34 | 0 | 28 | 18 |
0 | 0 | 0 | 34 | 23 | 13 |
0 | 0 | 13 | 23 | 7 | 0 |
0 | 0 | 18 | 28 | 0 | 7 |
1 | 0 | 0 | 0 | 0 | 0 |
1 | 40 | 0 | 0 | 0 | 0 |
0 | 0 | 40 | 0 | 0 | 0 |
0 | 0 | 35 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 6 | 40 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,6,35,0,0,0,0,6,1,0,0,0,0,0,0,6,35,0,0,0,0,6,1],[1,1,0,0,0,0,0,40,0,0,0,0,0,0,0,0,39,13,0,0,0,0,28,2,0,0,39,13,0,0,0,0,28,2,0,0],[40,40,0,0,0,0,2,1,0,0,0,0,0,0,0,0,1,6,0,0,0,0,0,40,0,0,40,35,0,0,0,0,0,1,0,0],[40,0,0,0,0,0,2,1,0,0,0,0,0,0,34,0,13,18,0,0,0,34,23,28,0,0,28,23,7,0,0,0,18,13,0,7],[1,1,0,0,0,0,0,40,0,0,0,0,0,0,40,35,0,0,0,0,0,1,0,0,0,0,0,0,1,6,0,0,0,0,0,40] >;
C10.322+ 1+4 in GAP, Magma, Sage, TeX
C_{10}._{32}2_+^{1+4}
% in TeX
G:=Group("C10.32ES+(2,2)");
// GroupNames label
G:=SmallGroup(320,1269);
// by ID
G=gap.SmallGroup(320,1269);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,387,1123,570,185,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=e^2=1,c^2=a^5,d^2=b^2,a*b=b*a,c*a*c^-1=e*a*e=a^-1,a*d=d*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