G = C10.432+ 1+4 order 320 = 26·5
43rd non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.432+ 1+4, C4⋊D4⋊17D5, C20⋊2D4⋊23C2, C4⋊C4.182D10, (D4×Dic5)⋊22C2, (C2×D4).156D10, C22⋊C4.49D10, C4.Dic10⋊19C2, Dic5⋊4D4⋊11C2, D10.53(C4○D4), C20.203(C4○D4), C4.96(D4⋊2D5), (C2×C20).596C23, (C2×C10).158C24, (C22×C4).225D10, C2.45(D4⋊6D10), C23.18(C22×D5), (D4×C10).124C22, C23.D10⋊19C2, C4⋊Dic5.372C22, (C22×C10).25C23, (C2×Dic5).77C23, C22.179(C23×D5), C23.D5.26C22, C23.18D10⋊11C2, C23.21D10⋊26C2, (C22×C20).243C22, C5⋊7(C22.47C24), (C4×Dic5).104C22, (C22×D5).201C23, D10⋊C4.127C22, C10.D4.139C22, (C22×Dic5).111C22, (D5×C4⋊C4)⋊23C2, (C4×C5⋊D4)⋊19C2, C2.42(D5×C4○D4), (C5×C4⋊D4)⋊20C2, (C2×C4×D5).95C22, C10.155(C2×C4○D4), C2.38(C2×D4⋊2D5), (C2×C4).40(C22×D5), (C5×C4⋊C4).146C22, (C2×C5⋊D4).31C22, (C5×C22⋊C4).15C22, SmallGroup(320,1286)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.432+ 1+4
G = < a,b,c,d,e | a10=b4=c2=1, d2=a5b2, e2=a5, bab-1=a-1, ac=ca, ad=da, ae=ea, cbc=a5b-1, bd=db, ebe-1=a5b, cd=dc, ece-1=a5c, ede-1=b2d >
Subgroups: 790 in 238 conjugacy classes, 97 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C5, C2×C4, C2×C4, C2×C4, D4, 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, Dic5, C20, C20, D10, D10, C2×C10, C2×C10, C2×C4⋊C4, C42⋊C2, C4×D4, C4⋊D4, C4⋊D4, C22.D4, C42.C2, C42⋊2C2, C4×D5, C2×Dic5, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C2×C20, C2×C20, C5×D4, C22×D5, C22×C10, C22×C10, C22.47C24, C4×Dic5, C4×Dic5, C10.D4, C10.D4, C4⋊Dic5, C4⋊Dic5, D10⋊C4, C23.D5, C23.D5, C5×C22⋊C4, C5×C4⋊C4, C2×C4×D5, C2×C4×D5, C22×Dic5, C2×C5⋊D4, C2×C5⋊D4, C22×C20, D4×C10, D4×C10, C23.D10, Dic5⋊4D4, C4.Dic10, D5×C4⋊C4, C23.21D10, C4×C5⋊D4, D4×Dic5, C23.18D10, C20⋊2D4, C20⋊2D4, C5×C4⋊D4, C10.432+ 1+4
Quotients: C1, C2, C22, C23, D5, C4○D4, C24, D10, C2×C4○D4, 2+ 1+4, C22×D5, C22.47C24, D4⋊2D5, C23×D5, C2×D4⋊2D5, D4⋊6D10, D5×C4○D4, C10.432+ 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 16 25 151)(2 15 26 160)(3 14 27 159)(4 13 28 158)(5 12 29 157)(6 11 30 156)(7 20 21 155)(8 19 22 154)(9 18 23 153)(10 17 24 152)(31 136 50 145)(32 135 41 144)(33 134 42 143)(34 133 43 142)(35 132 44 141)(36 131 45 150)(37 140 46 149)(38 139 47 148)(39 138 48 147)(40 137 49 146)(51 125 70 116)(52 124 61 115)(53 123 62 114)(54 122 63 113)(55 121 64 112)(56 130 65 111)(57 129 66 120)(58 128 67 119)(59 127 68 118)(60 126 69 117)(71 96 90 105)(72 95 81 104)(73 94 82 103)(74 93 83 102)(75 92 84 101)(76 91 85 110)(77 100 86 109)(78 99 87 108)(79 98 88 107)(80 97 89 106)
(1 36)(2 37)(3 38)(4 39)(5 40)(6 31)(7 32)(8 33)(9 34)(10 35)(11 150)(12 141)(13 142)(14 143)(15 144)(16 145)(17 146)(18 147)(19 148)(20 149)(21 41)(22 42)(23 43)(24 44)(25 45)(26 46)(27 47)(28 48)(29 49)(30 50)(51 76)(52 77)(53 78)(54 79)(55 80)(56 71)(57 72)(58 73)(59 74)(60 75)(61 86)(62 87)(63 88)(64 89)(65 90)(66 81)(67 82)(68 83)(69 84)(70 85)(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)(131 156)(132 157)(133 158)(134 159)(135 160)(136 151)(137 152)(138 153)(139 154)(140 155)
(1 130 30 116)(2 121 21 117)(3 122 22 118)(4 123 23 119)(5 124 24 120)(6 125 25 111)(7 126 26 112)(8 127 27 113)(9 128 28 114)(10 129 29 115)(11 70 151 56)(12 61 152 57)(13 62 153 58)(14 63 154 59)(15 64 155 60)(16 65 156 51)(17 66 157 52)(18 67 158 53)(19 68 159 54)(20 69 160 55)(31 105 45 91)(32 106 46 92)(33 107 47 93)(34 108 48 94)(35 109 49 95)(36 110 50 96)(37 101 41 97)(38 102 42 98)(39 103 43 99)(40 104 44 100)(71 150 85 136)(72 141 86 137)(73 142 87 138)(74 143 88 139)(75 144 89 140)(76 145 90 131)(77 146 81 132)(78 147 82 133)(79 148 83 134)(80 149 84 135)
(1 145 6 150)(2 146 7 141)(3 147 8 142)(4 148 9 143)(5 149 10 144)(11 31 16 36)(12 32 17 37)(13 33 18 38)(14 34 19 39)(15 35 20 40)(21 132 26 137)(22 133 27 138)(23 134 28 139)(24 135 29 140)(25 136 30 131)(41 152 46 157)(42 153 47 158)(43 154 48 159)(44 155 49 160)(45 156 50 151)(51 105 56 110)(52 106 57 101)(53 107 58 102)(54 108 59 103)(55 109 60 104)(61 97 66 92)(62 98 67 93)(63 99 68 94)(64 100 69 95)(65 91 70 96)(71 125 76 130)(72 126 77 121)(73 127 78 122)(74 128 79 123)(75 129 80 124)(81 117 86 112)(82 118 87 113)(83 119 88 114)(84 120 89 115)(85 111 90 116)
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), (1,16,25,151)(2,15,26,160)(3,14,27,159)(4,13,28,158)(5,12,29,157)(6,11,30,156)(7,20,21,155)(8,19,22,154)(9,18,23,153)(10,17,24,152)(31,136,50,145)(32,135,41,144)(33,134,42,143)(34,133,43,142)(35,132,44,141)(36,131,45,150)(37,140,46,149)(38,139,47,148)(39,138,48,147)(40,137,49,146)(51,125,70,116)(52,124,61,115)(53,123,62,114)(54,122,63,113)(55,121,64,112)(56,130,65,111)(57,129,66,120)(58,128,67,119)(59,127,68,118)(60,126,69,117)(71,96,90,105)(72,95,81,104)(73,94,82,103)(74,93,83,102)(75,92,84,101)(76,91,85,110)(77,100,86,109)(78,99,87,108)(79,98,88,107)(80,97,89,106), (1,36)(2,37)(3,38)(4,39)(5,40)(6,31)(7,32)(8,33)(9,34)(10,35)(11,150)(12,141)(13,142)(14,143)(15,144)(16,145)(17,146)(18,147)(19,148)(20,149)(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(51,76)(52,77)(53,78)(54,79)(55,80)(56,71)(57,72)(58,73)(59,74)(60,75)(61,86)(62,87)(63,88)(64,89)(65,90)(66,81)(67,82)(68,83)(69,84)(70,85)(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)(131,156)(132,157)(133,158)(134,159)(135,160)(136,151)(137,152)(138,153)(139,154)(140,155), (1,130,30,116)(2,121,21,117)(3,122,22,118)(4,123,23,119)(5,124,24,120)(6,125,25,111)(7,126,26,112)(8,127,27,113)(9,128,28,114)(10,129,29,115)(11,70,151,56)(12,61,152,57)(13,62,153,58)(14,63,154,59)(15,64,155,60)(16,65,156,51)(17,66,157,52)(18,67,158,53)(19,68,159,54)(20,69,160,55)(31,105,45,91)(32,106,46,92)(33,107,47,93)(34,108,48,94)(35,109,49,95)(36,110,50,96)(37,101,41,97)(38,102,42,98)(39,103,43,99)(40,104,44,100)(71,150,85,136)(72,141,86,137)(73,142,87,138)(74,143,88,139)(75,144,89,140)(76,145,90,131)(77,146,81,132)(78,147,82,133)(79,148,83,134)(80,149,84,135), (1,145,6,150)(2,146,7,141)(3,147,8,142)(4,148,9,143)(5,149,10,144)(11,31,16,36)(12,32,17,37)(13,33,18,38)(14,34,19,39)(15,35,20,40)(21,132,26,137)(22,133,27,138)(23,134,28,139)(24,135,29,140)(25,136,30,131)(41,152,46,157)(42,153,47,158)(43,154,48,159)(44,155,49,160)(45,156,50,151)(51,105,56,110)(52,106,57,101)(53,107,58,102)(54,108,59,103)(55,109,60,104)(61,97,66,92)(62,98,67,93)(63,99,68,94)(64,100,69,95)(65,91,70,96)(71,125,76,130)(72,126,77,121)(73,127,78,122)(74,128,79,123)(75,129,80,124)(81,117,86,112)(82,118,87,113)(83,119,88,114)(84,120,89,115)(85,111,90,116)>;
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), (1,16,25,151)(2,15,26,160)(3,14,27,159)(4,13,28,158)(5,12,29,157)(6,11,30,156)(7,20,21,155)(8,19,22,154)(9,18,23,153)(10,17,24,152)(31,136,50,145)(32,135,41,144)(33,134,42,143)(34,133,43,142)(35,132,44,141)(36,131,45,150)(37,140,46,149)(38,139,47,148)(39,138,48,147)(40,137,49,146)(51,125,70,116)(52,124,61,115)(53,123,62,114)(54,122,63,113)(55,121,64,112)(56,130,65,111)(57,129,66,120)(58,128,67,119)(59,127,68,118)(60,126,69,117)(71,96,90,105)(72,95,81,104)(73,94,82,103)(74,93,83,102)(75,92,84,101)(76,91,85,110)(77,100,86,109)(78,99,87,108)(79,98,88,107)(80,97,89,106), (1,36)(2,37)(3,38)(4,39)(5,40)(6,31)(7,32)(8,33)(9,34)(10,35)(11,150)(12,141)(13,142)(14,143)(15,144)(16,145)(17,146)(18,147)(19,148)(20,149)(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(51,76)(52,77)(53,78)(54,79)(55,80)(56,71)(57,72)(58,73)(59,74)(60,75)(61,86)(62,87)(63,88)(64,89)(65,90)(66,81)(67,82)(68,83)(69,84)(70,85)(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)(131,156)(132,157)(133,158)(134,159)(135,160)(136,151)(137,152)(138,153)(139,154)(140,155), (1,130,30,116)(2,121,21,117)(3,122,22,118)(4,123,23,119)(5,124,24,120)(6,125,25,111)(7,126,26,112)(8,127,27,113)(9,128,28,114)(10,129,29,115)(11,70,151,56)(12,61,152,57)(13,62,153,58)(14,63,154,59)(15,64,155,60)(16,65,156,51)(17,66,157,52)(18,67,158,53)(19,68,159,54)(20,69,160,55)(31,105,45,91)(32,106,46,92)(33,107,47,93)(34,108,48,94)(35,109,49,95)(36,110,50,96)(37,101,41,97)(38,102,42,98)(39,103,43,99)(40,104,44,100)(71,150,85,136)(72,141,86,137)(73,142,87,138)(74,143,88,139)(75,144,89,140)(76,145,90,131)(77,146,81,132)(78,147,82,133)(79,148,83,134)(80,149,84,135), (1,145,6,150)(2,146,7,141)(3,147,8,142)(4,148,9,143)(5,149,10,144)(11,31,16,36)(12,32,17,37)(13,33,18,38)(14,34,19,39)(15,35,20,40)(21,132,26,137)(22,133,27,138)(23,134,28,139)(24,135,29,140)(25,136,30,131)(41,152,46,157)(42,153,47,158)(43,154,48,159)(44,155,49,160)(45,156,50,151)(51,105,56,110)(52,106,57,101)(53,107,58,102)(54,108,59,103)(55,109,60,104)(61,97,66,92)(62,98,67,93)(63,99,68,94)(64,100,69,95)(65,91,70,96)(71,125,76,130)(72,126,77,121)(73,127,78,122)(74,128,79,123)(75,129,80,124)(81,117,86,112)(82,118,87,113)(83,119,88,114)(84,120,89,115)(85,111,90,116) );
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)], [(1,16,25,151),(2,15,26,160),(3,14,27,159),(4,13,28,158),(5,12,29,157),(6,11,30,156),(7,20,21,155),(8,19,22,154),(9,18,23,153),(10,17,24,152),(31,136,50,145),(32,135,41,144),(33,134,42,143),(34,133,43,142),(35,132,44,141),(36,131,45,150),(37,140,46,149),(38,139,47,148),(39,138,48,147),(40,137,49,146),(51,125,70,116),(52,124,61,115),(53,123,62,114),(54,122,63,113),(55,121,64,112),(56,130,65,111),(57,129,66,120),(58,128,67,119),(59,127,68,118),(60,126,69,117),(71,96,90,105),(72,95,81,104),(73,94,82,103),(74,93,83,102),(75,92,84,101),(76,91,85,110),(77,100,86,109),(78,99,87,108),(79,98,88,107),(80,97,89,106)], [(1,36),(2,37),(3,38),(4,39),(5,40),(6,31),(7,32),(8,33),(9,34),(10,35),(11,150),(12,141),(13,142),(14,143),(15,144),(16,145),(17,146),(18,147),(19,148),(20,149),(21,41),(22,42),(23,43),(24,44),(25,45),(26,46),(27,47),(28,48),(29,49),(30,50),(51,76),(52,77),(53,78),(54,79),(55,80),(56,71),(57,72),(58,73),(59,74),(60,75),(61,86),(62,87),(63,88),(64,89),(65,90),(66,81),(67,82),(68,83),(69,84),(70,85),(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),(131,156),(132,157),(133,158),(134,159),(135,160),(136,151),(137,152),(138,153),(139,154),(140,155)], [(1,130,30,116),(2,121,21,117),(3,122,22,118),(4,123,23,119),(5,124,24,120),(6,125,25,111),(7,126,26,112),(8,127,27,113),(9,128,28,114),(10,129,29,115),(11,70,151,56),(12,61,152,57),(13,62,153,58),(14,63,154,59),(15,64,155,60),(16,65,156,51),(17,66,157,52),(18,67,158,53),(19,68,159,54),(20,69,160,55),(31,105,45,91),(32,106,46,92),(33,107,47,93),(34,108,48,94),(35,109,49,95),(36,110,50,96),(37,101,41,97),(38,102,42,98),(39,103,43,99),(40,104,44,100),(71,150,85,136),(72,141,86,137),(73,142,87,138),(74,143,88,139),(75,144,89,140),(76,145,90,131),(77,146,81,132),(78,147,82,133),(79,148,83,134),(80,149,84,135)], [(1,145,6,150),(2,146,7,141),(3,147,8,142),(4,148,9,143),(5,149,10,144),(11,31,16,36),(12,32,17,37),(13,33,18,38),(14,34,19,39),(15,35,20,40),(21,132,26,137),(22,133,27,138),(23,134,28,139),(24,135,29,140),(25,136,30,131),(41,152,46,157),(42,153,47,158),(43,154,48,159),(44,155,49,160),(45,156,50,151),(51,105,56,110),(52,106,57,101),(53,107,58,102),(54,108,59,103),(55,109,60,104),(61,97,66,92),(62,98,67,93),(63,99,68,94),(64,100,69,95),(65,91,70,96),(71,125,76,130),(72,126,77,121),(73,127,78,122),(74,128,79,123),(75,129,80,124),(81,117,86,112),(82,118,87,113),(83,119,88,114),(84,120,89,115),(85,111,90,116)]])
53 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | 4G | ··· | 4L | 4M | 4N | 4O | 4P | 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 | 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 | 4 | 4 | 4 | 10 | 10 | 2 | 2 | 2 | 2 | 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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D5 | C4○D4 | C4○D4 | D10 | D10 | D10 | D10 | 2+ 1+4 | D4⋊2D5 | D4⋊6D10 | D5×C4○D4 |
| kernel | C10.432+ 1+4 | C23.D10 | Dic5⋊4D4 | C4.Dic10 | D5×C4⋊C4 | C23.21D10 | C4×C5⋊D4 | D4×Dic5 | C23.18D10 | C20⋊2D4 | C5×C4⋊D4 | C4⋊D4 | C20 | D10 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C10 | C4 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 3 | 1 | 2 | 4 | 4 | 4 | 2 | 2 | 6 | 1 | 4 | 4 | 4 |
Matrix representation of C10.432+ 1+4 ►in GL6(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 35 | 0 | 0 |
| 0 | 0 | 7 | 34 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 32 | 0 | 0 | 0 | 0 |
| 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 40 | 0 | 0 |
| 0 | 0 | 7 | 34 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 40 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 39 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 0 | 0 | 9 |
| 32 | 0 | 0 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 39 |
| 0 | 0 | 0 | 0 | 1 | 40 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,0,7,0,0,0,0,35,34,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[0,32,0,0,0,0,32,0,0,0,0,0,0,0,7,7,0,0,0,0,40,34,0,0,0,0,0,0,40,40,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,39,40],[0,40,0,0,0,0,40,0,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,9,0,0,0,0,0,0,9],[32,0,0,0,0,0,0,9,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,1,0,0,0,0,39,40] >;
C10.432+ 1+4 in GAP, Magma, Sage, TeX
C_{10}._{43}2_+^{1+4} % in TeX
G:=Group("C10.43ES+(2,2)"); // GroupNames label
G:=SmallGroup(320,1286);
// by ID
G=gap.SmallGroup(320,1286);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,232,387,100,1571,185,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=c^2=1,d^2=a^5*b^2,e^2=a^5,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=a^5*b^-1,b*d=d*b,e*b*e^-1=a^5*b,c*d=d*c,e*c*e^-1=a^5*c,e*d*e^-1=b^2*d>;
// generators/relations