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G = C3×C34⋊C2  order 486 = 2·35

Direct product of C3 and C34⋊C2

direct product, metabelian, supersoluble, monomial, A-group

Aliases: C3×C34⋊C2, C35⋊4C2, C34⋊16S3, C34⋊17C6, C33⋊20(C3×S3), C33⋊12(C3⋊S3), C32⋊3(C33⋊C2), C3⋊(C3×C33⋊C2), C32⋊6(C3×C3⋊S3), SmallGroup(486,259)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C34 — C3×C34⋊C2
Chief series
C1 — C3 — C32 — C33 — C34 — C35 — C3×C34⋊C2
Lower central
C34 — C3×C34⋊C2
Upper central
C1 — C3

Generators and relations for C3×C34⋊C2
 G = < a,b,c,d,e,f | a3=b3=c3=d3=e3=f2=1, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, fbf=b-1, cd=dc, ce=ec, fcf=c-1, de=ed, fdf=d-1, fef=e-1 >

Subgroups: 7568 in 1968 conjugacy classes, 426 normal (6 characteristic)
C1, C2, C3, C3, C3, S3, C6, C32, C32, C3×S3, C3⋊S3, C33, C33, C3×C3⋊S3, C33⋊C2, C34, C34, C34, C3×C33⋊C2, C34⋊C2, C35, C3×C34⋊C2
Quotients: C1, C2, C3, S3, C6, C3×S3, C3⋊S3, C3×C3⋊S3, C33⋊C2, C3×C33⋊C2, C34⋊C2, C3×C34⋊C2

Smallest permutation representation of C3×C34⋊C2
►On 162 points
Generators in S162
(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 22 106)(2 23 107)(3 24 108)(4 19 13)(5 20 14)(6 21 15)(7 25 10)(8 26 11)(9 27 12)(16 39 75)(17 37 73)(18 38 74)(28 46 43)(29 47 44)(30 48 45)(31 61 121)(32 62 122)(33 63 123)(34 49 40)(35 50 41)(36 51 42)(52 90 99)(53 88 97)(54 89 98)(55 76 64)(56 77 65)(57 78 66)(58 79 70)(59 80 71)(60 81 72)(67 132 114)(68 130 112)(69 131 113)(82 91 100)(83 92 101)(84 93 102)(85 94 103)(86 95 104)(87 96 105)(109 118 127)(110 119 128)(111 120 129)(115 124 133)(116 125 134)(117 126 135)(136 145 154)(137 146 155)(138 147 156)(139 148 157)(140 149 158)(141 150 159)(142 151 160)(143 152 161)(144 153 162)

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

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

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

126 conjugacy classes

class 1  2 3A3B3C···3DR6A6B
order12333···366
size181112···28181

126 irreducible representations

dim111122
type+++
imageC1C2C3C6S3C3×S3
kernelC3×C34⋊C2C35C34⋊C2C34C34C33
# reps11224080

Matrix representation of C3×C34⋊C2 ►in GL8(𝔽7)

40000000
04000000
00400000
00040000
00002000
00000200
00000010
00000001
,
40000000
02000000
00400000
00020000
00004000
00000200
00000040
00000002
,
40000000
02000000
00200000
00040000
00004000
00000200
00000010
00000001
,
10000000
01000000
00400000
00020000
00002000
00000400
00000020
00000004
,
40000000
02000000
00200000
00040000
00001000
00000100
00000020
00000004
,
01000000
10000000
00010000
00100000
00000100
00001000
00000001
00000010

G:=sub<GL(8,GF(7))| [4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[4,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,2],[4,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,4],[4,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,4],[0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;
 

C3×C34⋊C2 in GAP, Magma, Sage, TeX 

C_3\times C_3^4\rtimes C_2
 
% in TeX
 
G:=Group("C3xC3^4:C2");
 
// GroupNames label
 
G:=SmallGroup(486,259);
 
// by ID
 
G=gap.SmallGroup(486,259);
 
# by ID
 
G:=PCGroup([6,-2,-3,-3,-3,-3,-3,218,867,3244,11669]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f|a^3=b^3=c^3=d^3=e^3=f^2=1,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,f*b*f=b^-1,c*d=d*c,c*e=e*c,f*c*f=c^-1,d*e=e*d,f*d*f=d^-1,f*e*f=e^-1>;
 
// generators/relations
 

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