direct product, metabelian, nilpotent (class 3), monomial, 3-elementary
Aliases: C2×C33.7C32, (C3×C6).20He3, C33.7(C3×C6), C32⋊C9.13C6, C6.5(He3.C3), (C32×C6).7C32, C32.35(C2×He3), (C2×C32⋊C9).4C3, C3.8(C2×He3.C3), SmallGroup(486,69)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C33.7C32
G = < a,b,c,d,e,f | a2=b3=c3=d3=1, e3=d-1, f3=c, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, ebe-1=bc-1, fbf-1=bd-1, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=bc-1d-1e >
Smallest permutation representation of C2×C33.7C32
►On 162 points
Generators in S162
(1 128)(2 129)(3 130)(4 131)(5 132)(6 133)(7 134)(8 135)(9 127)(10 143)(11 144)(12 136)(13 137)(14 138)(15 139)(16 140)(17 141)(18 142)(19 94)(20 95)(21 96)(22 97)(23 98)(24 99)(25 91)(26 92)(27 93)(28 89)(29 90)(30 82)(31 83)(32 84)(33 85)(34 86)(35 87)(36 88)(37 119)(38 120)(39 121)(40 122)(41 123)(42 124)(43 125)(44 126)(45 118)(46 108)(47 100)(48 101)(49 102)(50 103)(51 104)(52 105)(53 106)(54 107)(55 116)(56 117)(57 109)(58 110)(59 111)(60 112)(61 113)(62 114)(63 115)(64 145)(65 146)(66 147)(67 148)(68 149)(69 150)(70 151)(71 152)(72 153)(73 154)(74 155)(75 156)(76 157)(77 158)(78 159)(79 160)(80 161)(81 162)
(2 24 78)(3 79 25)(5 27 81)(6 73 19)(8 21 75)(9 76 22)(10 82 70)(11 17 14)(12 66 90)(13 85 64)(15 69 84)(16 88 67)(18 72 87)(28 34 31)(29 136 147)(30 151 143)(32 139 150)(33 145 137)(35 142 153)(36 148 140)(37 114 51)(38 49 109)(39 42 45)(40 117 54)(41 52 112)(43 111 48)(44 46 115)(47 50 53)(55 58 61)(56 107 122)(57 120 102)(59 101 125)(60 123 105)(62 104 119)(63 126 108)(65 71 68)(83 89 86)(91 130 160)(93 162 132)(94 133 154)(96 156 135)(97 127 157)(99 159 129)(100 103 106)(110 113 116)(118 121 124)(138 144 141)(146 152 149)
(1 77 23)(2 78 24)(3 79 25)(4 80 26)(5 81 27)(6 73 19)(7 74 20)(8 75 21)(9 76 22)(10 85 67)(11 86 68)(12 87 69)(13 88 70)(14 89 71)(15 90 72)(16 82 64)(17 83 65)(18 84 66)(28 152 138)(29 153 139)(30 145 140)(31 146 141)(32 147 142)(33 148 143)(34 149 144)(35 150 136)(36 151 137)(37 54 111)(38 46 112)(39 47 113)(40 48 114)(41 49 115)(42 50 116)(43 51 117)(44 52 109)(45 53 110)(55 124 103)(56 125 104)(57 126 105)(58 118 106)(59 119 107)(60 120 108)(61 121 100)(62 122 101)(63 123 102)(91 130 160)(92 131 161)(93 132 162)(94 133 154)(95 134 155)(96 135 156)(97 127 157)(98 128 158)(99 129 159)
(1 7 4)(2 8 5)(3 9 6)(10 16 13)(11 17 14)(12 18 15)(19 25 22)(20 26 23)(21 27 24)(28 34 31)(29 35 32)(30 36 33)(37 43 40)(38 44 41)(39 45 42)(46 52 49)(47 53 50)(48 54 51)(55 61 58)(56 62 59)(57 63 60)(64 70 67)(65 71 68)(66 72 69)(73 79 76)(74 80 77)(75 81 78)(82 88 85)(83 89 86)(84 90 87)(91 97 94)(92 98 95)(93 99 96)(100 106 103)(101 107 104)(102 108 105)(109 115 112)(110 116 113)(111 117 114)(118 124 121)(119 125 122)(120 126 123)(127 133 130)(128 134 131)(129 135 132)(136 142 139)(137 143 140)(138 144 141)(145 151 148)(146 152 149)(147 153 150)(154 160 157)(155 161 158)(156 162 159)
(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)(154 155 156 157 158 159 160 161 162)
(1 113 86 77 39 68 23 47 11)(2 37 12 78 54 87 24 111 69)(3 109 88 79 44 70 25 52 13)(4 116 89 80 42 71 26 50 14)(5 40 15 81 48 90 27 114 72)(6 112 82 73 38 64 19 46 16)(7 110 83 74 45 65 20 53 17)(8 43 18 75 51 84 21 117 66)(9 115 85 76 41 67 22 49 10)(28 161 124 152 92 103 138 131 55)(29 93 62 153 132 122 139 162 101)(30 154 120 145 94 108 140 133 60)(31 155 118 146 95 106 141 134 58)(32 96 56 147 135 125 142 156 104)(33 157 123 148 97 102 143 127 63)(34 158 121 149 98 100 144 128 61)(35 99 59 150 129 119 136 159 107)(36 160 126 151 91 105 137 130 57)
G:=sub<Sym(162)| (1,128)(2,129)(3,130)(4,131)(5,132)(6,133)(7,134)(8,135)(9,127)(10,143)(11,144)(12,136)(13,137)(14,138)(15,139)(16,140)(17,141)(18,142)(19,94)(20,95)(21,96)(22,97)(23,98)(24,99)(25,91)(26,92)(27,93)(28,89)(29,90)(30,82)(31,83)(32,84)(33,85)(34,86)(35,87)(36,88)(37,119)(38,120)(39,121)(40,122)(41,123)(42,124)(43,125)(44,126)(45,118)(46,108)(47,100)(48,101)(49,102)(50,103)(51,104)(52,105)(53,106)(54,107)(55,116)(56,117)(57,109)(58,110)(59,111)(60,112)(61,113)(62,114)(63,115)(64,145)(65,146)(66,147)(67,148)(68,149)(69,150)(70,151)(71,152)(72,153)(73,154)(74,155)(75,156)(76,157)(77,158)(78,159)(79,160)(80,161)(81,162), (2,24,78)(3,79,25)(5,27,81)(6,73,19)(8,21,75)(9,76,22)(10,82,70)(11,17,14)(12,66,90)(13,85,64)(15,69,84)(16,88,67)(18,72,87)(28,34,31)(29,136,147)(30,151,143)(32,139,150)(33,145,137)(35,142,153)(36,148,140)(37,114,51)(38,49,109)(39,42,45)(40,117,54)(41,52,112)(43,111,48)(44,46,115)(47,50,53)(55,58,61)(56,107,122)(57,120,102)(59,101,125)(60,123,105)(62,104,119)(63,126,108)(65,71,68)(83,89,86)(91,130,160)(93,162,132)(94,133,154)(96,156,135)(97,127,157)(99,159,129)(100,103,106)(110,113,116)(118,121,124)(138,144,141)(146,152,149), (1,77,23)(2,78,24)(3,79,25)(4,80,26)(5,81,27)(6,73,19)(7,74,20)(8,75,21)(9,76,22)(10,85,67)(11,86,68)(12,87,69)(13,88,70)(14,89,71)(15,90,72)(16,82,64)(17,83,65)(18,84,66)(28,152,138)(29,153,139)(30,145,140)(31,146,141)(32,147,142)(33,148,143)(34,149,144)(35,150,136)(36,151,137)(37,54,111)(38,46,112)(39,47,113)(40,48,114)(41,49,115)(42,50,116)(43,51,117)(44,52,109)(45,53,110)(55,124,103)(56,125,104)(57,126,105)(58,118,106)(59,119,107)(60,120,108)(61,121,100)(62,122,101)(63,123,102)(91,130,160)(92,131,161)(93,132,162)(94,133,154)(95,134,155)(96,135,156)(97,127,157)(98,128,158)(99,129,159), (1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15)(19,25,22)(20,26,23)(21,27,24)(28,34,31)(29,35,32)(30,36,33)(37,43,40)(38,44,41)(39,45,42)(46,52,49)(47,53,50)(48,54,51)(55,61,58)(56,62,59)(57,63,60)(64,70,67)(65,71,68)(66,72,69)(73,79,76)(74,80,77)(75,81,78)(82,88,85)(83,89,86)(84,90,87)(91,97,94)(92,98,95)(93,99,96)(100,106,103)(101,107,104)(102,108,105)(109,115,112)(110,116,113)(111,117,114)(118,124,121)(119,125,122)(120,126,123)(127,133,130)(128,134,131)(129,135,132)(136,142,139)(137,143,140)(138,144,141)(145,151,148)(146,152,149)(147,153,150)(154,160,157)(155,161,158)(156,162,159), (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)(154,155,156,157,158,159,160,161,162), (1,113,86,77,39,68,23,47,11)(2,37,12,78,54,87,24,111,69)(3,109,88,79,44,70,25,52,13)(4,116,89,80,42,71,26,50,14)(5,40,15,81,48,90,27,114,72)(6,112,82,73,38,64,19,46,16)(7,110,83,74,45,65,20,53,17)(8,43,18,75,51,84,21,117,66)(9,115,85,76,41,67,22,49,10)(28,161,124,152,92,103,138,131,55)(29,93,62,153,132,122,139,162,101)(30,154,120,145,94,108,140,133,60)(31,155,118,146,95,106,141,134,58)(32,96,56,147,135,125,142,156,104)(33,157,123,148,97,102,143,127,63)(34,158,121,149,98,100,144,128,61)(35,99,59,150,129,119,136,159,107)(36,160,126,151,91,105,137,130,57)>;
G:=Group( (1,128)(2,129)(3,130)(4,131)(5,132)(6,133)(7,134)(8,135)(9,127)(10,143)(11,144)(12,136)(13,137)(14,138)(15,139)(16,140)(17,141)(18,142)(19,94)(20,95)(21,96)(22,97)(23,98)(24,99)(25,91)(26,92)(27,93)(28,89)(29,90)(30,82)(31,83)(32,84)(33,85)(34,86)(35,87)(36,88)(37,119)(38,120)(39,121)(40,122)(41,123)(42,124)(43,125)(44,126)(45,118)(46,108)(47,100)(48,101)(49,102)(50,103)(51,104)(52,105)(53,106)(54,107)(55,116)(56,117)(57,109)(58,110)(59,111)(60,112)(61,113)(62,114)(63,115)(64,145)(65,146)(66,147)(67,148)(68,149)(69,150)(70,151)(71,152)(72,153)(73,154)(74,155)(75,156)(76,157)(77,158)(78,159)(79,160)(80,161)(81,162), (2,24,78)(3,79,25)(5,27,81)(6,73,19)(8,21,75)(9,76,22)(10,82,70)(11,17,14)(12,66,90)(13,85,64)(15,69,84)(16,88,67)(18,72,87)(28,34,31)(29,136,147)(30,151,143)(32,139,150)(33,145,137)(35,142,153)(36,148,140)(37,114,51)(38,49,109)(39,42,45)(40,117,54)(41,52,112)(43,111,48)(44,46,115)(47,50,53)(55,58,61)(56,107,122)(57,120,102)(59,101,125)(60,123,105)(62,104,119)(63,126,108)(65,71,68)(83,89,86)(91,130,160)(93,162,132)(94,133,154)(96,156,135)(97,127,157)(99,159,129)(100,103,106)(110,113,116)(118,121,124)(138,144,141)(146,152,149), (1,77,23)(2,78,24)(3,79,25)(4,80,26)(5,81,27)(6,73,19)(7,74,20)(8,75,21)(9,76,22)(10,85,67)(11,86,68)(12,87,69)(13,88,70)(14,89,71)(15,90,72)(16,82,64)(17,83,65)(18,84,66)(28,152,138)(29,153,139)(30,145,140)(31,146,141)(32,147,142)(33,148,143)(34,149,144)(35,150,136)(36,151,137)(37,54,111)(38,46,112)(39,47,113)(40,48,114)(41,49,115)(42,50,116)(43,51,117)(44,52,109)(45,53,110)(55,124,103)(56,125,104)(57,126,105)(58,118,106)(59,119,107)(60,120,108)(61,121,100)(62,122,101)(63,123,102)(91,130,160)(92,131,161)(93,132,162)(94,133,154)(95,134,155)(96,135,156)(97,127,157)(98,128,158)(99,129,159), (1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15)(19,25,22)(20,26,23)(21,27,24)(28,34,31)(29,35,32)(30,36,33)(37,43,40)(38,44,41)(39,45,42)(46,52,49)(47,53,50)(48,54,51)(55,61,58)(56,62,59)(57,63,60)(64,70,67)(65,71,68)(66,72,69)(73,79,76)(74,80,77)(75,81,78)(82,88,85)(83,89,86)(84,90,87)(91,97,94)(92,98,95)(93,99,96)(100,106,103)(101,107,104)(102,108,105)(109,115,112)(110,116,113)(111,117,114)(118,124,121)(119,125,122)(120,126,123)(127,133,130)(128,134,131)(129,135,132)(136,142,139)(137,143,140)(138,144,141)(145,151,148)(146,152,149)(147,153,150)(154,160,157)(155,161,158)(156,162,159), (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)(154,155,156,157,158,159,160,161,162), (1,113,86,77,39,68,23,47,11)(2,37,12,78,54,87,24,111,69)(3,109,88,79,44,70,25,52,13)(4,116,89,80,42,71,26,50,14)(5,40,15,81,48,90,27,114,72)(6,112,82,73,38,64,19,46,16)(7,110,83,74,45,65,20,53,17)(8,43,18,75,51,84,21,117,66)(9,115,85,76,41,67,22,49,10)(28,161,124,152,92,103,138,131,55)(29,93,62,153,132,122,139,162,101)(30,154,120,145,94,108,140,133,60)(31,155,118,146,95,106,141,134,58)(32,96,56,147,135,125,142,156,104)(33,157,123,148,97,102,143,127,63)(34,158,121,149,98,100,144,128,61)(35,99,59,150,129,119,136,159,107)(36,160,126,151,91,105,137,130,57) );
G=PermutationGroup([[(1,128),(2,129),(3,130),(4,131),(5,132),(6,133),(7,134),(8,135),(9,127),(10,143),(11,144),(12,136),(13,137),(14,138),(15,139),(16,140),(17,141),(18,142),(19,94),(20,95),(21,96),(22,97),(23,98),(24,99),(25,91),(26,92),(27,93),(28,89),(29,90),(30,82),(31,83),(32,84),(33,85),(34,86),(35,87),(36,88),(37,119),(38,120),(39,121),(40,122),(41,123),(42,124),(43,125),(44,126),(45,118),(46,108),(47,100),(48,101),(49,102),(50,103),(51,104),(52,105),(53,106),(54,107),(55,116),(56,117),(57,109),(58,110),(59,111),(60,112),(61,113),(62,114),(63,115),(64,145),(65,146),(66,147),(67,148),(68,149),(69,150),(70,151),(71,152),(72,153),(73,154),(74,155),(75,156),(76,157),(77,158),(78,159),(79,160),(80,161),(81,162)], [(2,24,78),(3,79,25),(5,27,81),(6,73,19),(8,21,75),(9,76,22),(10,82,70),(11,17,14),(12,66,90),(13,85,64),(15,69,84),(16,88,67),(18,72,87),(28,34,31),(29,136,147),(30,151,143),(32,139,150),(33,145,137),(35,142,153),(36,148,140),(37,114,51),(38,49,109),(39,42,45),(40,117,54),(41,52,112),(43,111,48),(44,46,115),(47,50,53),(55,58,61),(56,107,122),(57,120,102),(59,101,125),(60,123,105),(62,104,119),(63,126,108),(65,71,68),(83,89,86),(91,130,160),(93,162,132),(94,133,154),(96,156,135),(97,127,157),(99,159,129),(100,103,106),(110,113,116),(118,121,124),(138,144,141),(146,152,149)], [(1,77,23),(2,78,24),(3,79,25),(4,80,26),(5,81,27),(6,73,19),(7,74,20),(8,75,21),(9,76,22),(10,85,67),(11,86,68),(12,87,69),(13,88,70),(14,89,71),(15,90,72),(16,82,64),(17,83,65),(18,84,66),(28,152,138),(29,153,139),(30,145,140),(31,146,141),(32,147,142),(33,148,143),(34,149,144),(35,150,136),(36,151,137),(37,54,111),(38,46,112),(39,47,113),(40,48,114),(41,49,115),(42,50,116),(43,51,117),(44,52,109),(45,53,110),(55,124,103),(56,125,104),(57,126,105),(58,118,106),(59,119,107),(60,120,108),(61,121,100),(62,122,101),(63,123,102),(91,130,160),(92,131,161),(93,132,162),(94,133,154),(95,134,155),(96,135,156),(97,127,157),(98,128,158),(99,129,159)], [(1,7,4),(2,8,5),(3,9,6),(10,16,13),(11,17,14),(12,18,15),(19,25,22),(20,26,23),(21,27,24),(28,34,31),(29,35,32),(30,36,33),(37,43,40),(38,44,41),(39,45,42),(46,52,49),(47,53,50),(48,54,51),(55,61,58),(56,62,59),(57,63,60),(64,70,67),(65,71,68),(66,72,69),(73,79,76),(74,80,77),(75,81,78),(82,88,85),(83,89,86),(84,90,87),(91,97,94),(92,98,95),(93,99,96),(100,106,103),(101,107,104),(102,108,105),(109,115,112),(110,116,113),(111,117,114),(118,124,121),(119,125,122),(120,126,123),(127,133,130),(128,134,131),(129,135,132),(136,142,139),(137,143,140),(138,144,141),(145,151,148),(146,152,149),(147,153,150),(154,160,157),(155,161,158),(156,162,159)], [(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),(154,155,156,157,158,159,160,161,162)], [(1,113,86,77,39,68,23,47,11),(2,37,12,78,54,87,24,111,69),(3,109,88,79,44,70,25,52,13),(4,116,89,80,42,71,26,50,14),(5,40,15,81,48,90,27,114,72),(6,112,82,73,38,64,19,46,16),(7,110,83,74,45,65,20,53,17),(8,43,18,75,51,84,21,117,66),(9,115,85,76,41,67,22,49,10),(28,161,124,152,92,103,138,131,55),(29,93,62,153,132,122,139,162,101),(30,154,120,145,94,108,140,133,60),(31,155,118,146,95,106,141,134,58),(32,96,56,147,135,125,142,156,104),(33,157,123,148,97,102,143,127,63),(34,158,121,149,98,100,144,128,61),(35,99,59,150,129,119,136,159,107),(36,160,126,151,91,105,137,130,57)]])
70 conjugacy classes
| class | 1 | 2 | 3A | ··· | 3H | 3I | 3J | 6A | ··· | 6H | 6I | 6J | 9A | ··· | 9X | 18A | ··· | 18X |
| order | 1 | 2 | 3 | ··· | 3 | 3 | 3 | 6 | ··· | 6 | 6 | 6 | 9 | ··· | 9 | 18 | ··· | 18 |
| size | 1 | 1 | 1 | ··· | 1 | 9 | 9 | 1 | ··· | 1 | 9 | 9 | 9 | ··· | 9 | 9 | ··· | 9 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 3 | 3 | 3 | 3 |
| type | + | + | ||||||
| image | C1 | C2 | C3 | C6 | He3 | C2×He3 | He3.C3 | C2×He3.C3 |
| kernel | C2×C33.7C32 | C33.7C32 | C2×C32⋊C9 | C32⋊C9 | C3×C6 | C32 | C6 | C3 |
| # reps | 1 | 1 | 8 | 8 | 2 | 2 | 24 | 24 |
Matrix representation of C2×C33.7C32 ►in GL7(𝔽19)
| 18 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 11 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 11 | 0 |
| 0 | 0 | 0 | 0 | 11 | 12 | 7 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 7 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 7 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 11 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 11 |
| 7 | 0 | 0 | 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 | 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 6 | 4 | 9 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 6 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 12 | 8 | 10 |
| 0 | 0 | 0 | 0 | 0 | 0 | 11 |
G:=sub<GL(7,GF(19))| [18,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,1,0,11,0,0,0,0,0,11,12,0,0,0,0,0,0,7],[1,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,11],[7,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,4,0,6,0,0,0,0,0,4,4,0,0,0,0,0,0,9],[1,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,12,0,0,0,0,0,1,8,0,0,0,0,0,0,10,11] >;
C2×C33.7C32 in GAP, Magma, Sage, TeX
C_2\times C_3^3._7C_3^2
% in TeX
G:=Group("C2xC3^3.7C3^2"); // GroupNames label
G:=SmallGroup(486,69);
// by ID
G=gap.SmallGroup(486,69);
# by ID
G:=PCGroup([6,-2,-3,-3,-3,-3,-3,1951,224,176,873,735]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^3=c^3=d^3=1,e^3=d^-1,f^3=c,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,e*b*e^-1=b*c^-1,f*b*f^-1=b*d^-1,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=b*c^-1*d^-1*e>;
// generators/relations
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