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## G = C2×C33.7C32order 486 = 2·35

### Direct product of C2 and C33.7C32

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

 Derived series C1 — C33 — C2×C33.7C32
 Chief series C1 — C3 — C32 — C33 — C32⋊C9 — C33.7C32 — C2×C33.7C32
 Lower central C1 — C32 — C33 — C2×C33.7C32
 Upper central C1 — C3×C6 — C32×C6 — C2×C33.7C32

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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