G = C10.732- 1+4 order 320 = 26·5
28th non-split extension by C10 of 2- 1+4 acting via 2- 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.732- 1+4, C5⋊D4⋊3D4, C20⋊Q8⋊20C2, C4⋊D4⋊14D5, C5⋊4(D4⋊6D4), C20⋊10(C4○D4), C4⋊4(D4⋊2D5), C20⋊2D4⋊20C2, C22.7(D4×D5), C4⋊C4.181D10, (D4×Dic5)⋊21C2, D10.41(C2×D4), C22⋊C4.9D10, (C2×D4).155D10, Dic5.47(C2×D4), C10.70(C22×D4), (C2×C20).174C23, (C2×C10).155C24, (C22×C4).224D10, D10.12D4⋊19C2, (D4×C10).123C22, C4⋊Dic5.371C22, (C22×C10).22C23, C22.176(C23×D5), C23.183(C22×D5), Dic5.14D4⋊20C2, C23.18D10⋊10C2, (C22×C20).242C22, (C4×Dic5).103C22, (C2×Dic5).238C23, (C22×D5).199C23, C23.D5.111C22, C2.31(D4.10D10), D10⋊C4.105C22, (C2×Dic10).161C22, C10.D4.117C22, (C22×Dic5).110C22, C2.43(C2×D4×D5), (D5×C4⋊C4)⋊22C2, (C4×C5⋊D4)⋊17C2, (C2×C10).7(C2×D4), (C5×C4⋊D4)⋊17C2, (C2×C4⋊Dic5)⋊40C2, C10.84(C2×C4○D4), (C2×D4⋊2D5)⋊15C2, (C2×C4×D5).93C22, C2.37(C2×D4⋊2D5), (C5×C4⋊C4).145C22, (C2×C4).587(C22×D5), (C2×C5⋊D4).29C22, (C5×C22⋊C4).14C22, SmallGroup(320,1283)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.732- 1+4
G = < a,b,c,d,e | a10=b4=c2=1, d2=b2, e2=a5b2, bab-1=dad-1=a-1, ac=ca, ae=ea, cbc=b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=a5b2d >
Subgroups: 982 in 292 conjugacy classes, 107 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C5, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, C23, D5, C10, C10, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic5, Dic5, C20, C20, D10, D10, C2×C10, C2×C10, C2×C10, C2×C4⋊C4, C4×D4, C4⋊D4, C4⋊D4, C22⋊Q8, C22.D4, C4⋊Q8, C2×C4○D4, Dic10, C4×D5, C2×Dic5, C2×Dic5, C2×Dic5, C5⋊D4, C5⋊D4, C2×C20, C2×C20, C2×C20, C5×D4, C22×D5, C22×C10, C22×C10, D4⋊6D4, C4×Dic5, C10.D4, C10.D4, C4⋊Dic5, C4⋊Dic5, D10⋊C4, C23.D5, C23.D5, C5×C22⋊C4, C5×C4⋊C4, C2×Dic10, C2×C4×D5, C2×C4×D5, D4⋊2D5, C22×Dic5, C2×C5⋊D4, C2×C5⋊D4, C22×C20, D4×C10, D4×C10, Dic5.14D4, D10.12D4, C20⋊Q8, D5×C4⋊C4, C2×C4⋊Dic5, C4×C5⋊D4, D4×Dic5, C23.18D10, C20⋊2D4, C5×C4⋊D4, C2×D4⋊2D5, C10.732- 1+4
Quotients: C1, C2, C22, D4, C23, D5, C2×D4, C4○D4, C24, D10, C22×D4, C2×C4○D4, 2- 1+4, C22×D5, D4⋊6D4, D4×D5, D4⋊2D5, C23×D5, C2×D4×D5, C2×D4⋊2D5, D4.10D10, C10.732- 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 38 30 50)(2 37 21 49)(3 36 22 48)(4 35 23 47)(5 34 24 46)(6 33 25 45)(7 32 26 44)(8 31 27 43)(9 40 28 42)(10 39 29 41)(11 138 153 150)(12 137 154 149)(13 136 155 148)(14 135 156 147)(15 134 157 146)(16 133 158 145)(17 132 159 144)(18 131 160 143)(19 140 151 142)(20 139 152 141)(51 80 63 82)(52 79 64 81)(53 78 65 90)(54 77 66 89)(55 76 67 88)(56 75 68 87)(57 74 69 86)(58 73 70 85)(59 72 61 84)(60 71 62 83)(91 122 103 120)(92 121 104 119)(93 130 105 118)(94 129 106 117)(95 128 107 116)(96 127 108 115)(97 126 109 114)(98 125 110 113)(99 124 101 112)(100 123 102 111)
(1 45)(2 46)(3 47)(4 48)(5 49)(6 50)(7 41)(8 42)(9 43)(10 44)(11 133)(12 134)(13 135)(14 136)(15 137)(16 138)(17 139)(18 140)(19 131)(20 132)(21 34)(22 35)(23 36)(24 37)(25 38)(26 39)(27 40)(28 31)(29 32)(30 33)(51 83)(52 84)(53 85)(54 86)(55 87)(56 88)(57 89)(58 90)(59 81)(60 82)(61 79)(62 80)(63 71)(64 72)(65 73)(66 74)(67 75)(68 76)(69 77)(70 78)(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)(141 159)(142 160)(143 151)(144 152)(145 153)(146 154)(147 155)(148 156)(149 157)(150 158)
(1 53 30 65)(2 52 21 64)(3 51 22 63)(4 60 23 62)(5 59 24 61)(6 58 25 70)(7 57 26 69)(8 56 27 68)(9 55 28 67)(10 54 29 66)(11 130 153 118)(12 129 154 117)(13 128 155 116)(14 127 156 115)(15 126 157 114)(16 125 158 113)(17 124 159 112)(18 123 160 111)(19 122 151 120)(20 121 152 119)(31 75 43 87)(32 74 44 86)(33 73 45 85)(34 72 46 84)(35 71 47 83)(36 80 48 82)(37 79 49 81)(38 78 50 90)(39 77 41 89)(40 76 42 88)(91 140 103 142)(92 139 104 141)(93 138 105 150)(94 137 106 149)(95 136 107 148)(96 135 108 147)(97 134 109 146)(98 133 110 145)(99 132 101 144)(100 131 102 143)
(1 98 25 105)(2 99 26 106)(3 100 27 107)(4 91 28 108)(5 92 29 109)(6 93 30 110)(7 94 21 101)(8 95 22 102)(9 96 23 103)(10 97 24 104)(11 85 158 78)(12 86 159 79)(13 87 160 80)(14 88 151 71)(15 89 152 72)(16 90 153 73)(17 81 154 74)(18 82 155 75)(19 83 156 76)(20 84 157 77)(31 128 48 111)(32 129 49 112)(33 130 50 113)(34 121 41 114)(35 122 42 115)(36 123 43 116)(37 124 44 117)(38 125 45 118)(39 126 46 119)(40 127 47 120)(51 148 68 131)(52 149 69 132)(53 150 70 133)(54 141 61 134)(55 142 62 135)(56 143 63 136)(57 144 64 137)(58 145 65 138)(59 146 66 139)(60 147 67 140)
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), (1,38,30,50)(2,37,21,49)(3,36,22,48)(4,35,23,47)(5,34,24,46)(6,33,25,45)(7,32,26,44)(8,31,27,43)(9,40,28,42)(10,39,29,41)(11,138,153,150)(12,137,154,149)(13,136,155,148)(14,135,156,147)(15,134,157,146)(16,133,158,145)(17,132,159,144)(18,131,160,143)(19,140,151,142)(20,139,152,141)(51,80,63,82)(52,79,64,81)(53,78,65,90)(54,77,66,89)(55,76,67,88)(56,75,68,87)(57,74,69,86)(58,73,70,85)(59,72,61,84)(60,71,62,83)(91,122,103,120)(92,121,104,119)(93,130,105,118)(94,129,106,117)(95,128,107,116)(96,127,108,115)(97,126,109,114)(98,125,110,113)(99,124,101,112)(100,123,102,111), (1,45)(2,46)(3,47)(4,48)(5,49)(6,50)(7,41)(8,42)(9,43)(10,44)(11,133)(12,134)(13,135)(14,136)(15,137)(16,138)(17,139)(18,140)(19,131)(20,132)(21,34)(22,35)(23,36)(24,37)(25,38)(26,39)(27,40)(28,31)(29,32)(30,33)(51,83)(52,84)(53,85)(54,86)(55,87)(56,88)(57,89)(58,90)(59,81)(60,82)(61,79)(62,80)(63,71)(64,72)(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(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)(141,159)(142,160)(143,151)(144,152)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158), (1,53,30,65)(2,52,21,64)(3,51,22,63)(4,60,23,62)(5,59,24,61)(6,58,25,70)(7,57,26,69)(8,56,27,68)(9,55,28,67)(10,54,29,66)(11,130,153,118)(12,129,154,117)(13,128,155,116)(14,127,156,115)(15,126,157,114)(16,125,158,113)(17,124,159,112)(18,123,160,111)(19,122,151,120)(20,121,152,119)(31,75,43,87)(32,74,44,86)(33,73,45,85)(34,72,46,84)(35,71,47,83)(36,80,48,82)(37,79,49,81)(38,78,50,90)(39,77,41,89)(40,76,42,88)(91,140,103,142)(92,139,104,141)(93,138,105,150)(94,137,106,149)(95,136,107,148)(96,135,108,147)(97,134,109,146)(98,133,110,145)(99,132,101,144)(100,131,102,143), (1,98,25,105)(2,99,26,106)(3,100,27,107)(4,91,28,108)(5,92,29,109)(6,93,30,110)(7,94,21,101)(8,95,22,102)(9,96,23,103)(10,97,24,104)(11,85,158,78)(12,86,159,79)(13,87,160,80)(14,88,151,71)(15,89,152,72)(16,90,153,73)(17,81,154,74)(18,82,155,75)(19,83,156,76)(20,84,157,77)(31,128,48,111)(32,129,49,112)(33,130,50,113)(34,121,41,114)(35,122,42,115)(36,123,43,116)(37,124,44,117)(38,125,45,118)(39,126,46,119)(40,127,47,120)(51,148,68,131)(52,149,69,132)(53,150,70,133)(54,141,61,134)(55,142,62,135)(56,143,63,136)(57,144,64,137)(58,145,65,138)(59,146,66,139)(60,147,67,140)>;
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), (1,38,30,50)(2,37,21,49)(3,36,22,48)(4,35,23,47)(5,34,24,46)(6,33,25,45)(7,32,26,44)(8,31,27,43)(9,40,28,42)(10,39,29,41)(11,138,153,150)(12,137,154,149)(13,136,155,148)(14,135,156,147)(15,134,157,146)(16,133,158,145)(17,132,159,144)(18,131,160,143)(19,140,151,142)(20,139,152,141)(51,80,63,82)(52,79,64,81)(53,78,65,90)(54,77,66,89)(55,76,67,88)(56,75,68,87)(57,74,69,86)(58,73,70,85)(59,72,61,84)(60,71,62,83)(91,122,103,120)(92,121,104,119)(93,130,105,118)(94,129,106,117)(95,128,107,116)(96,127,108,115)(97,126,109,114)(98,125,110,113)(99,124,101,112)(100,123,102,111), (1,45)(2,46)(3,47)(4,48)(5,49)(6,50)(7,41)(8,42)(9,43)(10,44)(11,133)(12,134)(13,135)(14,136)(15,137)(16,138)(17,139)(18,140)(19,131)(20,132)(21,34)(22,35)(23,36)(24,37)(25,38)(26,39)(27,40)(28,31)(29,32)(30,33)(51,83)(52,84)(53,85)(54,86)(55,87)(56,88)(57,89)(58,90)(59,81)(60,82)(61,79)(62,80)(63,71)(64,72)(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(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)(141,159)(142,160)(143,151)(144,152)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158), (1,53,30,65)(2,52,21,64)(3,51,22,63)(4,60,23,62)(5,59,24,61)(6,58,25,70)(7,57,26,69)(8,56,27,68)(9,55,28,67)(10,54,29,66)(11,130,153,118)(12,129,154,117)(13,128,155,116)(14,127,156,115)(15,126,157,114)(16,125,158,113)(17,124,159,112)(18,123,160,111)(19,122,151,120)(20,121,152,119)(31,75,43,87)(32,74,44,86)(33,73,45,85)(34,72,46,84)(35,71,47,83)(36,80,48,82)(37,79,49,81)(38,78,50,90)(39,77,41,89)(40,76,42,88)(91,140,103,142)(92,139,104,141)(93,138,105,150)(94,137,106,149)(95,136,107,148)(96,135,108,147)(97,134,109,146)(98,133,110,145)(99,132,101,144)(100,131,102,143), (1,98,25,105)(2,99,26,106)(3,100,27,107)(4,91,28,108)(5,92,29,109)(6,93,30,110)(7,94,21,101)(8,95,22,102)(9,96,23,103)(10,97,24,104)(11,85,158,78)(12,86,159,79)(13,87,160,80)(14,88,151,71)(15,89,152,72)(16,90,153,73)(17,81,154,74)(18,82,155,75)(19,83,156,76)(20,84,157,77)(31,128,48,111)(32,129,49,112)(33,130,50,113)(34,121,41,114)(35,122,42,115)(36,123,43,116)(37,124,44,117)(38,125,45,118)(39,126,46,119)(40,127,47,120)(51,148,68,131)(52,149,69,132)(53,150,70,133)(54,141,61,134)(55,142,62,135)(56,143,63,136)(57,144,64,137)(58,145,65,138)(59,146,66,139)(60,147,67,140) );
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)], [(1,38,30,50),(2,37,21,49),(3,36,22,48),(4,35,23,47),(5,34,24,46),(6,33,25,45),(7,32,26,44),(8,31,27,43),(9,40,28,42),(10,39,29,41),(11,138,153,150),(12,137,154,149),(13,136,155,148),(14,135,156,147),(15,134,157,146),(16,133,158,145),(17,132,159,144),(18,131,160,143),(19,140,151,142),(20,139,152,141),(51,80,63,82),(52,79,64,81),(53,78,65,90),(54,77,66,89),(55,76,67,88),(56,75,68,87),(57,74,69,86),(58,73,70,85),(59,72,61,84),(60,71,62,83),(91,122,103,120),(92,121,104,119),(93,130,105,118),(94,129,106,117),(95,128,107,116),(96,127,108,115),(97,126,109,114),(98,125,110,113),(99,124,101,112),(100,123,102,111)], [(1,45),(2,46),(3,47),(4,48),(5,49),(6,50),(7,41),(8,42),(9,43),(10,44),(11,133),(12,134),(13,135),(14,136),(15,137),(16,138),(17,139),(18,140),(19,131),(20,132),(21,34),(22,35),(23,36),(24,37),(25,38),(26,39),(27,40),(28,31),(29,32),(30,33),(51,83),(52,84),(53,85),(54,86),(55,87),(56,88),(57,89),(58,90),(59,81),(60,82),(61,79),(62,80),(63,71),(64,72),(65,73),(66,74),(67,75),(68,76),(69,77),(70,78),(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),(141,159),(142,160),(143,151),(144,152),(145,153),(146,154),(147,155),(148,156),(149,157),(150,158)], [(1,53,30,65),(2,52,21,64),(3,51,22,63),(4,60,23,62),(5,59,24,61),(6,58,25,70),(7,57,26,69),(8,56,27,68),(9,55,28,67),(10,54,29,66),(11,130,153,118),(12,129,154,117),(13,128,155,116),(14,127,156,115),(15,126,157,114),(16,125,158,113),(17,124,159,112),(18,123,160,111),(19,122,151,120),(20,121,152,119),(31,75,43,87),(32,74,44,86),(33,73,45,85),(34,72,46,84),(35,71,47,83),(36,80,48,82),(37,79,49,81),(38,78,50,90),(39,77,41,89),(40,76,42,88),(91,140,103,142),(92,139,104,141),(93,138,105,150),(94,137,106,149),(95,136,107,148),(96,135,108,147),(97,134,109,146),(98,133,110,145),(99,132,101,144),(100,131,102,143)], [(1,98,25,105),(2,99,26,106),(3,100,27,107),(4,91,28,108),(5,92,29,109),(6,93,30,110),(7,94,21,101),(8,95,22,102),(9,96,23,103),(10,97,24,104),(11,85,158,78),(12,86,159,79),(13,87,160,80),(14,88,151,71),(15,89,152,72),(16,90,153,73),(17,81,154,74),(18,82,155,75),(19,83,156,76),(20,84,157,77),(31,128,48,111),(32,129,49,112),(33,130,50,113),(34,121,41,114),(35,122,42,115),(36,123,43,116),(37,124,44,117),(38,125,45,118),(39,126,46,119),(40,127,47,120),(51,148,68,131),(52,149,69,132),(53,150,70,133),(54,141,61,134),(55,142,62,135),(56,143,63,136),(57,144,64,137),(58,145,65,138),(59,146,66,139),(60,147,67,140)]])
53 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | ··· | 4K | 4L | 4M | 4N | 4O | 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 | 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 | 10 | 10 | 2 | 2 | 4 | 4 | 4 | 10 | ··· | 10 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | 8 | 8 | 8 |
53 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D5 | C4○D4 | D10 | D10 | D10 | D10 | 2- 1+4 | D4⋊2D5 | D4×D5 | D4.10D10 |
| kernel | C10.732- 1+4 | Dic5.14D4 | D10.12D4 | C20⋊Q8 | D5×C4⋊C4 | C2×C4⋊Dic5 | C4×C5⋊D4 | D4×Dic5 | C23.18D10 | C20⋊2D4 | C5×C4⋊D4 | C2×D4⋊2D5 | C5⋊D4 | C4⋊D4 | C20 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C10 | C4 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 2 | 4 | 2 | 4 | 4 | 2 | 2 | 6 | 1 | 4 | 4 | 4 |
Matrix representation of C10.732- 1+4 ►in GL6(𝔽41)
| 6 | 7 | 0 | 0 | 0 | 0 |
| 35 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 6 | 7 | 0 | 0 | 0 | 0 |
| 36 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 35 | 34 | 0 | 0 | 0 | 0 |
| 5 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 32 | 0 | 0 | 0 |
| 0 | 0 | 0 | 32 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 22 |
| 0 | 0 | 0 | 0 | 19 | 14 |
G:=sub<GL(6,GF(41))| [6,35,0,0,0,0,7,0,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[6,36,0,0,0,0,7,35,0,0,0,0,0,0,0,1,0,0,0,0,40,0,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[35,5,0,0,0,0,34,6,0,0,0,0,0,0,32,0,0,0,0,0,0,32,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,27,19,0,0,0,0,22,14] >;
C10.732- 1+4 in GAP, Magma, Sage, TeX
C_{10}._{73}2_-^{1+4} % in TeX
G:=Group("C10.73ES-(2,2)"); // GroupNames label
G:=SmallGroup(320,1283);
// by ID
G=gap.SmallGroup(320,1283);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,387,100,675,185,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=c^2=1,d^2=b^2,e^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=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=a^5*b^2*d>;
// generators/relations