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## G = C3×C34⋊C2order 486 = 2·35

### Direct product of C3 and C34⋊C2

Aliases: C3×C34⋊C2, C354C2, C3416S3, C3417C6, C3320(C3×S3), C3312(C3⋊S3), C323(C33⋊C2), C3⋊(C3×C33⋊C2), C326(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 3A 3B 3C ··· 3DR 6A 6B order 1 2 3 3 3 ··· 3 6 6 size 1 81 1 1 2 ··· 2 81 81

126 irreducible representations

 dim 1 1 1 1 2 2 type + + + image C1 C2 C3 C6 S3 C3×S3 kernel C3×C34⋊C2 C35 C34⋊C2 C34 C34 C33 # reps 1 1 2 2 40 80

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

 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

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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