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## G = C2×C33.3C32order 486 = 2·35

### Direct product of C2 and C33.3C32

direct product, metabelian, nilpotent (class 3), monomial, 3-elementary

Series: Derived Chief Lower central Upper central

 Derived series C1 — C33 — C2×C33.3C32
 Chief series C1 — C3 — C32 — C33 — C32⋊C9 — C33.3C32 — C2×C33.3C32
 Lower central C1 — C32 — C33 — C2×C33.3C32
 Upper central C1 — C3×C6 — C32×C6 — C2×C33.3C32

Generators and relations for C2×C33.3C32
G = < a,b,c,d,e,f | a2=b3=c3=e3=1, d3=f3=b, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, bf=fb, ede-1=cd=dc, ce=ec, cf=fc, fdf-1=bde-1, fef-1=b-1e >

Subgroups: 180 in 60 conjugacy classes, 24 normal (all characteristic)
C1, C2, C3, C3, C6, C6, C9, C32, C32, C18, C3×C6, C3×C6, C3×C9, 3- 1+2, C33, C3×C18, C2×3- 1+2, C32×C6, C32⋊C9, C3×3- 1+2, C2×C32⋊C9, C6×3- 1+2, C33.3C32, C2×C33.3C32
Quotients: C1, C2, C3, C6, C32, C3×C6, He3, C2×He3, C3≀C3, He3.C3, C3.He3, C2×C3≀C3, C2×He3.C3, C2×C3.He3, C33.3C32, C2×C33.3C32

Smallest permutation representation of C2×C33.3C32
On 162 points
Generators in S162
(1 100)(2 101)(3 102)(4 103)(5 104)(6 105)(7 106)(8 107)(9 108)(10 84)(11 85)(12 86)(13 87)(14 88)(15 89)(16 90)(17 82)(18 83)(19 93)(20 94)(21 95)(22 96)(23 97)(24 98)(25 99)(26 91)(27 92)(28 109)(29 110)(30 111)(31 112)(32 113)(33 114)(34 115)(35 116)(36 117)(37 118)(38 119)(39 120)(40 121)(41 122)(42 123)(43 124)(44 125)(45 126)(46 127)(47 128)(48 129)(49 130)(50 131)(51 132)(52 133)(53 134)(54 135)(55 136)(56 137)(57 138)(58 139)(59 140)(60 141)(61 142)(62 143)(63 144)(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)
(1 4 7)(2 5 8)(3 6 9)(10 13 16)(11 14 17)(12 15 18)(19 22 25)(20 23 26)(21 24 27)(28 31 34)(29 32 35)(30 33 36)(37 40 43)(38 41 44)(39 42 45)(46 49 52)(47 50 53)(48 51 54)(55 58 61)(56 59 62)(57 60 63)(64 67 70)(65 68 71)(66 69 72)(73 76 79)(74 77 80)(75 78 81)(82 85 88)(83 86 89)(84 87 90)(91 94 97)(92 95 98)(93 96 99)(100 103 106)(101 104 107)(102 105 108)(109 112 115)(110 113 116)(111 114 117)(118 121 124)(119 122 125)(120 123 126)(127 130 133)(128 131 134)(129 132 135)(136 139 142)(137 140 143)(138 141 144)(145 148 151)(146 149 152)(147 150 153)(154 157 160)(155 158 161)(156 159 162)
(1 43 36)(2 44 28)(3 45 29)(4 37 30)(5 38 31)(6 39 32)(7 40 33)(8 41 34)(9 42 35)(10 155 23)(11 156 24)(12 157 25)(13 158 26)(14 159 27)(15 160 19)(16 161 20)(17 162 21)(18 154 22)(46 56 66)(47 57 67)(48 58 68)(49 59 69)(50 60 70)(51 61 71)(52 62 72)(53 63 64)(54 55 65)(73 96 83)(74 97 84)(75 98 85)(76 99 86)(77 91 87)(78 92 88)(79 93 89)(80 94 90)(81 95 82)(100 124 117)(101 125 109)(102 126 110)(103 118 111)(104 119 112)(105 120 113)(106 121 114)(107 122 115)(108 123 116)(127 137 147)(128 138 148)(129 139 149)(130 140 150)(131 141 151)(132 142 152)(133 143 153)(134 144 145)(135 136 146)
(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)
(2 28 44)(3 45 29)(5 31 38)(6 39 32)(8 34 41)(9 42 35)(10 161 26)(11 17 14)(12 22 160)(13 155 20)(15 25 154)(16 158 23)(18 19 157)(21 27 24)(46 49 52)(47 70 63)(48 61 65)(50 64 57)(51 55 68)(53 67 60)(54 58 71)(56 59 62)(66 69 72)(73 89 99)(74 94 87)(75 81 78)(76 83 93)(77 97 90)(79 86 96)(80 91 84)(82 88 85)(92 98 95)(101 109 125)(102 126 110)(104 112 119)(105 120 113)(107 115 122)(108 123 116)(127 130 133)(128 151 144)(129 142 146)(131 145 138)(132 136 149)(134 148 141)(135 139 152)(137 140 143)(147 150 153)(156 162 159)
(1 95 49 4 98 52 7 92 46)(2 79 60 5 73 63 8 76 57)(3 91 51 6 94 54 9 97 48)(10 139 126 13 142 120 16 136 123)(11 143 121 14 137 124 17 140 118)(12 128 109 15 131 112 18 134 115)(19 151 119 22 145 122 25 148 125)(20 135 108 23 129 102 26 132 105)(21 130 103 24 133 106 27 127 100)(28 89 50 31 83 53 34 86 47)(29 77 71 32 80 65 35 74 68)(30 75 72 33 78 66 36 81 69)(37 85 62 40 88 56 43 82 59)(38 96 64 41 99 67 44 93 70)(39 90 55 42 84 58 45 87 61)(101 160 141 104 154 144 107 157 138)(110 158 152 113 161 146 116 155 149)(111 156 153 114 159 147 117 162 150)

G:=sub<Sym(162)| (1,100)(2,101)(3,102)(4,103)(5,104)(6,105)(7,106)(8,107)(9,108)(10,84)(11,85)(12,86)(13,87)(14,88)(15,89)(16,90)(17,82)(18,83)(19,93)(20,94)(21,95)(22,96)(23,97)(24,98)(25,99)(26,91)(27,92)(28,109)(29,110)(30,111)(31,112)(32,113)(33,114)(34,115)(35,116)(36,117)(37,118)(38,119)(39,120)(40,121)(41,122)(42,123)(43,124)(44,125)(45,126)(46,127)(47,128)(48,129)(49,130)(50,131)(51,132)(52,133)(53,134)(54,135)(55,136)(56,137)(57,138)(58,139)(59,140)(60,141)(61,142)(62,143)(63,144)(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), (1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,14,17)(12,15,18)(19,22,25)(20,23,26)(21,24,27)(28,31,34)(29,32,35)(30,33,36)(37,40,43)(38,41,44)(39,42,45)(46,49,52)(47,50,53)(48,51,54)(55,58,61)(56,59,62)(57,60,63)(64,67,70)(65,68,71)(66,69,72)(73,76,79)(74,77,80)(75,78,81)(82,85,88)(83,86,89)(84,87,90)(91,94,97)(92,95,98)(93,96,99)(100,103,106)(101,104,107)(102,105,108)(109,112,115)(110,113,116)(111,114,117)(118,121,124)(119,122,125)(120,123,126)(127,130,133)(128,131,134)(129,132,135)(136,139,142)(137,140,143)(138,141,144)(145,148,151)(146,149,152)(147,150,153)(154,157,160)(155,158,161)(156,159,162), (1,43,36)(2,44,28)(3,45,29)(4,37,30)(5,38,31)(6,39,32)(7,40,33)(8,41,34)(9,42,35)(10,155,23)(11,156,24)(12,157,25)(13,158,26)(14,159,27)(15,160,19)(16,161,20)(17,162,21)(18,154,22)(46,56,66)(47,57,67)(48,58,68)(49,59,69)(50,60,70)(51,61,71)(52,62,72)(53,63,64)(54,55,65)(73,96,83)(74,97,84)(75,98,85)(76,99,86)(77,91,87)(78,92,88)(79,93,89)(80,94,90)(81,95,82)(100,124,117)(101,125,109)(102,126,110)(103,118,111)(104,119,112)(105,120,113)(106,121,114)(107,122,115)(108,123,116)(127,137,147)(128,138,148)(129,139,149)(130,140,150)(131,141,151)(132,142,152)(133,143,153)(134,144,145)(135,136,146), (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), (2,28,44)(3,45,29)(5,31,38)(6,39,32)(8,34,41)(9,42,35)(10,161,26)(11,17,14)(12,22,160)(13,155,20)(15,25,154)(16,158,23)(18,19,157)(21,27,24)(46,49,52)(47,70,63)(48,61,65)(50,64,57)(51,55,68)(53,67,60)(54,58,71)(56,59,62)(66,69,72)(73,89,99)(74,94,87)(75,81,78)(76,83,93)(77,97,90)(79,86,96)(80,91,84)(82,88,85)(92,98,95)(101,109,125)(102,126,110)(104,112,119)(105,120,113)(107,115,122)(108,123,116)(127,130,133)(128,151,144)(129,142,146)(131,145,138)(132,136,149)(134,148,141)(135,139,152)(137,140,143)(147,150,153)(156,162,159), (1,95,49,4,98,52,7,92,46)(2,79,60,5,73,63,8,76,57)(3,91,51,6,94,54,9,97,48)(10,139,126,13,142,120,16,136,123)(11,143,121,14,137,124,17,140,118)(12,128,109,15,131,112,18,134,115)(19,151,119,22,145,122,25,148,125)(20,135,108,23,129,102,26,132,105)(21,130,103,24,133,106,27,127,100)(28,89,50,31,83,53,34,86,47)(29,77,71,32,80,65,35,74,68)(30,75,72,33,78,66,36,81,69)(37,85,62,40,88,56,43,82,59)(38,96,64,41,99,67,44,93,70)(39,90,55,42,84,58,45,87,61)(101,160,141,104,154,144,107,157,138)(110,158,152,113,161,146,116,155,149)(111,156,153,114,159,147,117,162,150)>;

G:=Group( (1,100)(2,101)(3,102)(4,103)(5,104)(6,105)(7,106)(8,107)(9,108)(10,84)(11,85)(12,86)(13,87)(14,88)(15,89)(16,90)(17,82)(18,83)(19,93)(20,94)(21,95)(22,96)(23,97)(24,98)(25,99)(26,91)(27,92)(28,109)(29,110)(30,111)(31,112)(32,113)(33,114)(34,115)(35,116)(36,117)(37,118)(38,119)(39,120)(40,121)(41,122)(42,123)(43,124)(44,125)(45,126)(46,127)(47,128)(48,129)(49,130)(50,131)(51,132)(52,133)(53,134)(54,135)(55,136)(56,137)(57,138)(58,139)(59,140)(60,141)(61,142)(62,143)(63,144)(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), (1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,14,17)(12,15,18)(19,22,25)(20,23,26)(21,24,27)(28,31,34)(29,32,35)(30,33,36)(37,40,43)(38,41,44)(39,42,45)(46,49,52)(47,50,53)(48,51,54)(55,58,61)(56,59,62)(57,60,63)(64,67,70)(65,68,71)(66,69,72)(73,76,79)(74,77,80)(75,78,81)(82,85,88)(83,86,89)(84,87,90)(91,94,97)(92,95,98)(93,96,99)(100,103,106)(101,104,107)(102,105,108)(109,112,115)(110,113,116)(111,114,117)(118,121,124)(119,122,125)(120,123,126)(127,130,133)(128,131,134)(129,132,135)(136,139,142)(137,140,143)(138,141,144)(145,148,151)(146,149,152)(147,150,153)(154,157,160)(155,158,161)(156,159,162), (1,43,36)(2,44,28)(3,45,29)(4,37,30)(5,38,31)(6,39,32)(7,40,33)(8,41,34)(9,42,35)(10,155,23)(11,156,24)(12,157,25)(13,158,26)(14,159,27)(15,160,19)(16,161,20)(17,162,21)(18,154,22)(46,56,66)(47,57,67)(48,58,68)(49,59,69)(50,60,70)(51,61,71)(52,62,72)(53,63,64)(54,55,65)(73,96,83)(74,97,84)(75,98,85)(76,99,86)(77,91,87)(78,92,88)(79,93,89)(80,94,90)(81,95,82)(100,124,117)(101,125,109)(102,126,110)(103,118,111)(104,119,112)(105,120,113)(106,121,114)(107,122,115)(108,123,116)(127,137,147)(128,138,148)(129,139,149)(130,140,150)(131,141,151)(132,142,152)(133,143,153)(134,144,145)(135,136,146), (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), (2,28,44)(3,45,29)(5,31,38)(6,39,32)(8,34,41)(9,42,35)(10,161,26)(11,17,14)(12,22,160)(13,155,20)(15,25,154)(16,158,23)(18,19,157)(21,27,24)(46,49,52)(47,70,63)(48,61,65)(50,64,57)(51,55,68)(53,67,60)(54,58,71)(56,59,62)(66,69,72)(73,89,99)(74,94,87)(75,81,78)(76,83,93)(77,97,90)(79,86,96)(80,91,84)(82,88,85)(92,98,95)(101,109,125)(102,126,110)(104,112,119)(105,120,113)(107,115,122)(108,123,116)(127,130,133)(128,151,144)(129,142,146)(131,145,138)(132,136,149)(134,148,141)(135,139,152)(137,140,143)(147,150,153)(156,162,159), (1,95,49,4,98,52,7,92,46)(2,79,60,5,73,63,8,76,57)(3,91,51,6,94,54,9,97,48)(10,139,126,13,142,120,16,136,123)(11,143,121,14,137,124,17,140,118)(12,128,109,15,131,112,18,134,115)(19,151,119,22,145,122,25,148,125)(20,135,108,23,129,102,26,132,105)(21,130,103,24,133,106,27,127,100)(28,89,50,31,83,53,34,86,47)(29,77,71,32,80,65,35,74,68)(30,75,72,33,78,66,36,81,69)(37,85,62,40,88,56,43,82,59)(38,96,64,41,99,67,44,93,70)(39,90,55,42,84,58,45,87,61)(101,160,141,104,154,144,107,157,138)(110,158,152,113,161,146,116,155,149)(111,156,153,114,159,147,117,162,150) );

G=PermutationGroup([[(1,100),(2,101),(3,102),(4,103),(5,104),(6,105),(7,106),(8,107),(9,108),(10,84),(11,85),(12,86),(13,87),(14,88),(15,89),(16,90),(17,82),(18,83),(19,93),(20,94),(21,95),(22,96),(23,97),(24,98),(25,99),(26,91),(27,92),(28,109),(29,110),(30,111),(31,112),(32,113),(33,114),(34,115),(35,116),(36,117),(37,118),(38,119),(39,120),(40,121),(41,122),(42,123),(43,124),(44,125),(45,126),(46,127),(47,128),(48,129),(49,130),(50,131),(51,132),(52,133),(53,134),(54,135),(55,136),(56,137),(57,138),(58,139),(59,140),(60,141),(61,142),(62,143),(63,144),(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)], [(1,4,7),(2,5,8),(3,6,9),(10,13,16),(11,14,17),(12,15,18),(19,22,25),(20,23,26),(21,24,27),(28,31,34),(29,32,35),(30,33,36),(37,40,43),(38,41,44),(39,42,45),(46,49,52),(47,50,53),(48,51,54),(55,58,61),(56,59,62),(57,60,63),(64,67,70),(65,68,71),(66,69,72),(73,76,79),(74,77,80),(75,78,81),(82,85,88),(83,86,89),(84,87,90),(91,94,97),(92,95,98),(93,96,99),(100,103,106),(101,104,107),(102,105,108),(109,112,115),(110,113,116),(111,114,117),(118,121,124),(119,122,125),(120,123,126),(127,130,133),(128,131,134),(129,132,135),(136,139,142),(137,140,143),(138,141,144),(145,148,151),(146,149,152),(147,150,153),(154,157,160),(155,158,161),(156,159,162)], [(1,43,36),(2,44,28),(3,45,29),(4,37,30),(5,38,31),(6,39,32),(7,40,33),(8,41,34),(9,42,35),(10,155,23),(11,156,24),(12,157,25),(13,158,26),(14,159,27),(15,160,19),(16,161,20),(17,162,21),(18,154,22),(46,56,66),(47,57,67),(48,58,68),(49,59,69),(50,60,70),(51,61,71),(52,62,72),(53,63,64),(54,55,65),(73,96,83),(74,97,84),(75,98,85),(76,99,86),(77,91,87),(78,92,88),(79,93,89),(80,94,90),(81,95,82),(100,124,117),(101,125,109),(102,126,110),(103,118,111),(104,119,112),(105,120,113),(106,121,114),(107,122,115),(108,123,116),(127,137,147),(128,138,148),(129,139,149),(130,140,150),(131,141,151),(132,142,152),(133,143,153),(134,144,145),(135,136,146)], [(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)], [(2,28,44),(3,45,29),(5,31,38),(6,39,32),(8,34,41),(9,42,35),(10,161,26),(11,17,14),(12,22,160),(13,155,20),(15,25,154),(16,158,23),(18,19,157),(21,27,24),(46,49,52),(47,70,63),(48,61,65),(50,64,57),(51,55,68),(53,67,60),(54,58,71),(56,59,62),(66,69,72),(73,89,99),(74,94,87),(75,81,78),(76,83,93),(77,97,90),(79,86,96),(80,91,84),(82,88,85),(92,98,95),(101,109,125),(102,126,110),(104,112,119),(105,120,113),(107,115,122),(108,123,116),(127,130,133),(128,151,144),(129,142,146),(131,145,138),(132,136,149),(134,148,141),(135,139,152),(137,140,143),(147,150,153),(156,162,159)], [(1,95,49,4,98,52,7,92,46),(2,79,60,5,73,63,8,76,57),(3,91,51,6,94,54,9,97,48),(10,139,126,13,142,120,16,136,123),(11,143,121,14,137,124,17,140,118),(12,128,109,15,131,112,18,134,115),(19,151,119,22,145,122,25,148,125),(20,135,108,23,129,102,26,132,105),(21,130,103,24,133,106,27,127,100),(28,89,50,31,83,53,34,86,47),(29,77,71,32,80,65,35,74,68),(30,75,72,33,78,66,36,81,69),(37,85,62,40,88,56,43,82,59),(38,96,64,41,99,67,44,93,70),(39,90,55,42,84,58,45,87,61),(101,160,141,104,154,144,107,157,138),(110,158,152,113,161,146,116,155,149),(111,156,153,114,159,147,117,162,150)]])

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 1 1 3 3 3 3 3 3 3 3 type + + image C1 C2 C3 C3 C6 C6 He3 C2×He3 C3≀C3 He3.C3 C3.He3 C2×C3≀C3 C2×He3.C3 C2×C3.He3 kernel C2×C33.3C32 C33.3C32 C2×C32⋊C9 C6×3- 1+2 C32⋊C9 C3×3- 1+2 C3×C6 C32 C6 C6 C6 C3 C3 C3 # reps 1 1 6 2 6 2 2 2 6 12 6 6 12 6

Matrix representation of C2×C33.3C32 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 11 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 11
,
 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 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 7
,
 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 11 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 7 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 11
,
 1 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 5 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 17 0 0 0 0 16 0 0 0 0 0 0 0 5 0

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],[1,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,11],[1,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,7],[1,0,0,0,0,0,0,0,0,0,11,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,11,0,0,0,0,1,0,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,11],[1,0,0,0,0,0,0,0,0,0,5,0,0,0,0,5,0,0,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,5,0,0,0,0,17,0,0] >;

C2×C33.3C32 in GAP, Magma, Sage, TeX

C_2\times C_3^3._3C_3^2
% in TeX

G:=Group("C2xC3^3.3C3^2");
// GroupNames label

G:=SmallGroup(486,65);
// by ID

G=gap.SmallGroup(486,65);
# by ID

G:=PCGroup([6,-2,-3,-3,-3,-3,-3,331,224,176,873,735]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^3=c^3=e^3=1,d^3=f^3=b,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,b*e=e*b,b*f=f*b,e*d*e^-1=c*d=d*c,c*e=e*c,c*f=f*c,f*d*f^-1=b*d*e^-1,f*e*f^-1=b^-1*e>;
// generators/relations

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