direct product, metabelian, supersoluble, monomial, A-group
Aliases: S3×C34, C35⋊1C2, C34⋊14C6, C3⋊(C33×C6), C33⋊13(C3×C6), C32⋊3(C32×C6), SmallGroup(486,256)
Series: Derived ►Chief ►Lower central ►Upper central
| C3 — S3×C34 |
Generators and relations for S3×C34
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, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef=e-1 >
Subgroups: 3512 in 1968 conjugacy classes, 636 normal (6 characteristic)
C1, C2, C3, C3, C3, S3, C6, C32, C32, C3×S3, C3×C6, C33, C33, S3×C32, C32×C6, C34, C34, C34, S3×C33, C33×C6, C35, S3×C34
Quotients: C1, C2, C3, S3, C6, C32, C3×S3, C3×C6, C33, S3×C32, C32×C6, C34, S3×C33, C33×C6, S3×C34
►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 47 18)(2 48 16)(3 46 17)(4 65 36)(5 66 34)(6 64 35)(7 60 39)(8 58 37)(9 59 38)(10 61 32)(11 62 33)(12 63 31)(13 71 45)(14 72 43)(15 70 44)(19 68 42)(20 69 40)(21 67 41)(22 80 54)(23 81 52)(24 79 53)(25 74 111)(26 75 109)(27 73 110)(28 157 131)(29 158 132)(30 159 130)(49 83 78)(50 84 76)(51 82 77)(55 106 155)(56 107 156)(57 108 154)(85 143 117)(86 144 115)(87 142 116)(88 137 120)(89 138 118)(90 136 119)(91 140 114)(92 141 112)(93 139 113)(94 152 126)(95 153 124)(96 151 125)(97 146 129)(98 147 127)(99 145 128)(100 149 123)(101 150 121)(102 148 122)(103 161 135)(104 162 133)(105 160 134)
(1 59 22)(2 60 23)(3 58 24)(4 51 15)(5 49 13)(6 50 14)(7 52 16)(8 53 17)(9 54 18)(10 111 21)(11 109 19)(12 110 20)(25 67 61)(26 68 62)(27 69 63)(28 153 120)(29 151 118)(30 152 119)(31 73 40)(32 74 41)(33 75 42)(34 78 45)(35 76 43)(36 77 44)(37 79 46)(38 80 47)(39 81 48)(55 102 144)(56 100 142)(57 101 143)(64 84 72)(65 82 70)(66 83 71)(85 154 121)(86 155 122)(87 156 123)(88 157 124)(89 158 125)(90 159 126)(91 160 127)(92 161 128)(93 162 129)(94 136 130)(95 137 131)(96 138 132)(97 139 133)(98 140 134)(99 141 135)(103 145 112)(104 146 113)(105 147 114)(106 148 115)(107 149 116)(108 150 117)
(1 74 4)(2 75 5)(3 73 6)(7 68 78)(8 69 76)(9 67 77)(10 70 80)(11 71 81)(12 72 79)(13 23 33)(14 24 31)(15 22 32)(16 26 34)(17 27 35)(18 25 36)(19 83 39)(20 84 37)(21 82 38)(28 91 101)(29 92 102)(30 93 100)(40 50 58)(41 51 59)(42 49 60)(43 53 63)(44 54 61)(45 52 62)(46 110 64)(47 111 65)(48 109 66)(55 118 128)(56 119 129)(57 120 127)(85 95 105)(86 96 103)(87 94 104)(88 98 108)(89 99 106)(90 97 107)(112 122 132)(113 123 130)(114 121 131)(115 125 135)(116 126 133)(117 124 134)(136 146 156)(137 147 154)(138 145 155)(139 149 159)(140 150 157)(141 148 158)(142 152 162)(143 153 160)(144 151 161)
(1 74 4)(2 75 5)(3 73 6)(7 68 78)(8 69 76)(9 67 77)(10 70 80)(11 71 81)(12 72 79)(13 23 33)(14 24 31)(15 22 32)(16 26 34)(17 27 35)(18 25 36)(19 83 39)(20 84 37)(21 82 38)(28 101 91)(29 102 92)(30 100 93)(40 50 58)(41 51 59)(42 49 60)(43 53 63)(44 54 61)(45 52 62)(46 110 64)(47 111 65)(48 109 66)(55 128 118)(56 129 119)(57 127 120)(85 105 95)(86 103 96)(87 104 94)(88 108 98)(89 106 99)(90 107 97)(112 132 122)(113 130 123)(114 131 121)(115 135 125)(116 133 126)(117 134 124)(136 156 146)(137 154 147)(138 155 145)(139 159 149)(140 157 150)(141 158 148)(142 162 152)(143 160 153)(144 161 151)
(1 145)(2 146)(3 147)(4 138)(5 136)(6 137)(7 139)(8 140)(9 141)(10 144)(11 142)(12 143)(13 94)(14 95)(15 96)(16 97)(17 98)(18 99)(19 100)(20 101)(21 102)(22 103)(23 104)(24 105)(25 106)(26 107)(27 108)(28 84)(29 82)(30 83)(31 85)(32 86)(33 87)(34 90)(35 88)(36 89)(37 91)(38 92)(39 93)(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)(55 111)(56 109)(57 110)(58 114)(59 112)(60 113)(61 115)(62 116)(63 117)(64 120)(65 118)(66 119)(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)
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), (1,47,18)(2,48,16)(3,46,17)(4,65,36)(5,66,34)(6,64,35)(7,60,39)(8,58,37)(9,59,38)(10,61,32)(11,62,33)(12,63,31)(13,71,45)(14,72,43)(15,70,44)(19,68,42)(20,69,40)(21,67,41)(22,80,54)(23,81,52)(24,79,53)(25,74,111)(26,75,109)(27,73,110)(28,157,131)(29,158,132)(30,159,130)(49,83,78)(50,84,76)(51,82,77)(55,106,155)(56,107,156)(57,108,154)(85,143,117)(86,144,115)(87,142,116)(88,137,120)(89,138,118)(90,136,119)(91,140,114)(92,141,112)(93,139,113)(94,152,126)(95,153,124)(96,151,125)(97,146,129)(98,147,127)(99,145,128)(100,149,123)(101,150,121)(102,148,122)(103,161,135)(104,162,133)(105,160,134), (1,59,22)(2,60,23)(3,58,24)(4,51,15)(5,49,13)(6,50,14)(7,52,16)(8,53,17)(9,54,18)(10,111,21)(11,109,19)(12,110,20)(25,67,61)(26,68,62)(27,69,63)(28,153,120)(29,151,118)(30,152,119)(31,73,40)(32,74,41)(33,75,42)(34,78,45)(35,76,43)(36,77,44)(37,79,46)(38,80,47)(39,81,48)(55,102,144)(56,100,142)(57,101,143)(64,84,72)(65,82,70)(66,83,71)(85,154,121)(86,155,122)(87,156,123)(88,157,124)(89,158,125)(90,159,126)(91,160,127)(92,161,128)(93,162,129)(94,136,130)(95,137,131)(96,138,132)(97,139,133)(98,140,134)(99,141,135)(103,145,112)(104,146,113)(105,147,114)(106,148,115)(107,149,116)(108,150,117), (1,74,4)(2,75,5)(3,73,6)(7,68,78)(8,69,76)(9,67,77)(10,70,80)(11,71,81)(12,72,79)(13,23,33)(14,24,31)(15,22,32)(16,26,34)(17,27,35)(18,25,36)(19,83,39)(20,84,37)(21,82,38)(28,91,101)(29,92,102)(30,93,100)(40,50,58)(41,51,59)(42,49,60)(43,53,63)(44,54,61)(45,52,62)(46,110,64)(47,111,65)(48,109,66)(55,118,128)(56,119,129)(57,120,127)(85,95,105)(86,96,103)(87,94,104)(88,98,108)(89,99,106)(90,97,107)(112,122,132)(113,123,130)(114,121,131)(115,125,135)(116,126,133)(117,124,134)(136,146,156)(137,147,154)(138,145,155)(139,149,159)(140,150,157)(141,148,158)(142,152,162)(143,153,160)(144,151,161), (1,74,4)(2,75,5)(3,73,6)(7,68,78)(8,69,76)(9,67,77)(10,70,80)(11,71,81)(12,72,79)(13,23,33)(14,24,31)(15,22,32)(16,26,34)(17,27,35)(18,25,36)(19,83,39)(20,84,37)(21,82,38)(28,101,91)(29,102,92)(30,100,93)(40,50,58)(41,51,59)(42,49,60)(43,53,63)(44,54,61)(45,52,62)(46,110,64)(47,111,65)(48,109,66)(55,128,118)(56,129,119)(57,127,120)(85,105,95)(86,103,96)(87,104,94)(88,108,98)(89,106,99)(90,107,97)(112,132,122)(113,130,123)(114,131,121)(115,135,125)(116,133,126)(117,134,124)(136,156,146)(137,154,147)(138,155,145)(139,159,149)(140,157,150)(141,158,148)(142,162,152)(143,160,153)(144,161,151), (1,145)(2,146)(3,147)(4,138)(5,136)(6,137)(7,139)(8,140)(9,141)(10,144)(11,142)(12,143)(13,94)(14,95)(15,96)(16,97)(17,98)(18,99)(19,100)(20,101)(21,102)(22,103)(23,104)(24,105)(25,106)(26,107)(27,108)(28,84)(29,82)(30,83)(31,85)(32,86)(33,87)(34,90)(35,88)(36,89)(37,91)(38,92)(39,93)(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)(55,111)(56,109)(57,110)(58,114)(59,112)(60,113)(61,115)(62,116)(63,117)(64,120)(65,118)(66,119)(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)>;
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), (1,47,18)(2,48,16)(3,46,17)(4,65,36)(5,66,34)(6,64,35)(7,60,39)(8,58,37)(9,59,38)(10,61,32)(11,62,33)(12,63,31)(13,71,45)(14,72,43)(15,70,44)(19,68,42)(20,69,40)(21,67,41)(22,80,54)(23,81,52)(24,79,53)(25,74,111)(26,75,109)(27,73,110)(28,157,131)(29,158,132)(30,159,130)(49,83,78)(50,84,76)(51,82,77)(55,106,155)(56,107,156)(57,108,154)(85,143,117)(86,144,115)(87,142,116)(88,137,120)(89,138,118)(90,136,119)(91,140,114)(92,141,112)(93,139,113)(94,152,126)(95,153,124)(96,151,125)(97,146,129)(98,147,127)(99,145,128)(100,149,123)(101,150,121)(102,148,122)(103,161,135)(104,162,133)(105,160,134), (1,59,22)(2,60,23)(3,58,24)(4,51,15)(5,49,13)(6,50,14)(7,52,16)(8,53,17)(9,54,18)(10,111,21)(11,109,19)(12,110,20)(25,67,61)(26,68,62)(27,69,63)(28,153,120)(29,151,118)(30,152,119)(31,73,40)(32,74,41)(33,75,42)(34,78,45)(35,76,43)(36,77,44)(37,79,46)(38,80,47)(39,81,48)(55,102,144)(56,100,142)(57,101,143)(64,84,72)(65,82,70)(66,83,71)(85,154,121)(86,155,122)(87,156,123)(88,157,124)(89,158,125)(90,159,126)(91,160,127)(92,161,128)(93,162,129)(94,136,130)(95,137,131)(96,138,132)(97,139,133)(98,140,134)(99,141,135)(103,145,112)(104,146,113)(105,147,114)(106,148,115)(107,149,116)(108,150,117), (1,74,4)(2,75,5)(3,73,6)(7,68,78)(8,69,76)(9,67,77)(10,70,80)(11,71,81)(12,72,79)(13,23,33)(14,24,31)(15,22,32)(16,26,34)(17,27,35)(18,25,36)(19,83,39)(20,84,37)(21,82,38)(28,91,101)(29,92,102)(30,93,100)(40,50,58)(41,51,59)(42,49,60)(43,53,63)(44,54,61)(45,52,62)(46,110,64)(47,111,65)(48,109,66)(55,118,128)(56,119,129)(57,120,127)(85,95,105)(86,96,103)(87,94,104)(88,98,108)(89,99,106)(90,97,107)(112,122,132)(113,123,130)(114,121,131)(115,125,135)(116,126,133)(117,124,134)(136,146,156)(137,147,154)(138,145,155)(139,149,159)(140,150,157)(141,148,158)(142,152,162)(143,153,160)(144,151,161), (1,74,4)(2,75,5)(3,73,6)(7,68,78)(8,69,76)(9,67,77)(10,70,80)(11,71,81)(12,72,79)(13,23,33)(14,24,31)(15,22,32)(16,26,34)(17,27,35)(18,25,36)(19,83,39)(20,84,37)(21,82,38)(28,101,91)(29,102,92)(30,100,93)(40,50,58)(41,51,59)(42,49,60)(43,53,63)(44,54,61)(45,52,62)(46,110,64)(47,111,65)(48,109,66)(55,128,118)(56,129,119)(57,127,120)(85,105,95)(86,103,96)(87,104,94)(88,108,98)(89,106,99)(90,107,97)(112,132,122)(113,130,123)(114,131,121)(115,135,125)(116,133,126)(117,134,124)(136,156,146)(137,154,147)(138,155,145)(139,159,149)(140,157,150)(141,158,148)(142,162,152)(143,160,153)(144,161,151), (1,145)(2,146)(3,147)(4,138)(5,136)(6,137)(7,139)(8,140)(9,141)(10,144)(11,142)(12,143)(13,94)(14,95)(15,96)(16,97)(17,98)(18,99)(19,100)(20,101)(21,102)(22,103)(23,104)(24,105)(25,106)(26,107)(27,108)(28,84)(29,82)(30,83)(31,85)(32,86)(33,87)(34,90)(35,88)(36,89)(37,91)(38,92)(39,93)(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)(55,111)(56,109)(57,110)(58,114)(59,112)(60,113)(61,115)(62,116)(63,117)(64,120)(65,118)(66,119)(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) );
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)], [(1,47,18),(2,48,16),(3,46,17),(4,65,36),(5,66,34),(6,64,35),(7,60,39),(8,58,37),(9,59,38),(10,61,32),(11,62,33),(12,63,31),(13,71,45),(14,72,43),(15,70,44),(19,68,42),(20,69,40),(21,67,41),(22,80,54),(23,81,52),(24,79,53),(25,74,111),(26,75,109),(27,73,110),(28,157,131),(29,158,132),(30,159,130),(49,83,78),(50,84,76),(51,82,77),(55,106,155),(56,107,156),(57,108,154),(85,143,117),(86,144,115),(87,142,116),(88,137,120),(89,138,118),(90,136,119),(91,140,114),(92,141,112),(93,139,113),(94,152,126),(95,153,124),(96,151,125),(97,146,129),(98,147,127),(99,145,128),(100,149,123),(101,150,121),(102,148,122),(103,161,135),(104,162,133),(105,160,134)], [(1,59,22),(2,60,23),(3,58,24),(4,51,15),(5,49,13),(6,50,14),(7,52,16),(8,53,17),(9,54,18),(10,111,21),(11,109,19),(12,110,20),(25,67,61),(26,68,62),(27,69,63),(28,153,120),(29,151,118),(30,152,119),(31,73,40),(32,74,41),(33,75,42),(34,78,45),(35,76,43),(36,77,44),(37,79,46),(38,80,47),(39,81,48),(55,102,144),(56,100,142),(57,101,143),(64,84,72),(65,82,70),(66,83,71),(85,154,121),(86,155,122),(87,156,123),(88,157,124),(89,158,125),(90,159,126),(91,160,127),(92,161,128),(93,162,129),(94,136,130),(95,137,131),(96,138,132),(97,139,133),(98,140,134),(99,141,135),(103,145,112),(104,146,113),(105,147,114),(106,148,115),(107,149,116),(108,150,117)], [(1,74,4),(2,75,5),(3,73,6),(7,68,78),(8,69,76),(9,67,77),(10,70,80),(11,71,81),(12,72,79),(13,23,33),(14,24,31),(15,22,32),(16,26,34),(17,27,35),(18,25,36),(19,83,39),(20,84,37),(21,82,38),(28,91,101),(29,92,102),(30,93,100),(40,50,58),(41,51,59),(42,49,60),(43,53,63),(44,54,61),(45,52,62),(46,110,64),(47,111,65),(48,109,66),(55,118,128),(56,119,129),(57,120,127),(85,95,105),(86,96,103),(87,94,104),(88,98,108),(89,99,106),(90,97,107),(112,122,132),(113,123,130),(114,121,131),(115,125,135),(116,126,133),(117,124,134),(136,146,156),(137,147,154),(138,145,155),(139,149,159),(140,150,157),(141,148,158),(142,152,162),(143,153,160),(144,151,161)], [(1,74,4),(2,75,5),(3,73,6),(7,68,78),(8,69,76),(9,67,77),(10,70,80),(11,71,81),(12,72,79),(13,23,33),(14,24,31),(15,22,32),(16,26,34),(17,27,35),(18,25,36),(19,83,39),(20,84,37),(21,82,38),(28,101,91),(29,102,92),(30,100,93),(40,50,58),(41,51,59),(42,49,60),(43,53,63),(44,54,61),(45,52,62),(46,110,64),(47,111,65),(48,109,66),(55,128,118),(56,129,119),(57,127,120),(85,105,95),(86,103,96),(87,104,94),(88,108,98),(89,106,99),(90,107,97),(112,132,122),(113,130,123),(114,131,121),(115,135,125),(116,133,126),(117,134,124),(136,156,146),(137,154,147),(138,155,145),(139,159,149),(140,157,150),(141,158,148),(142,162,152),(143,160,153),(144,161,151)], [(1,145),(2,146),(3,147),(4,138),(5,136),(6,137),(7,139),(8,140),(9,141),(10,144),(11,142),(12,143),(13,94),(14,95),(15,96),(16,97),(17,98),(18,99),(19,100),(20,101),(21,102),(22,103),(23,104),(24,105),(25,106),(26,107),(27,108),(28,84),(29,82),(30,83),(31,85),(32,86),(33,87),(34,90),(35,88),(36,89),(37,91),(38,92),(39,93),(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),(55,111),(56,109),(57,110),(58,114),(59,112),(60,113),(61,115),(62,116),(63,117),(64,120),(65,118),(66,119),(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)]])
243 conjugacy classes
| class | 1 | 2 | 3A | ··· | 3CB | 3CC | ··· | 3FE | 6A | ··· | 6CB |
| order | 1 | 2 | 3 | ··· | 3 | 3 | ··· | 3 | 6 | ··· | 6 |
| size | 1 | 3 | 1 | ··· | 1 | 2 | ··· | 2 | 3 | ··· | 3 |
243 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | |||
| image | C1 | C2 | C3 | C6 | S3 | C3×S3 |
| kernel | S3×C34 | C35 | S3×C33 | C34 | C34 | C33 |
| # reps | 1 | 1 | 80 | 80 | 1 | 80 |
Matrix representation of S3×C34 ►in GL5(𝔽7)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 | 0 |
| 0 | 0 | 2 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 2 | 0 | 0 | 0 | 0 |
| 0 | 2 | 0 | 0 | 0 |
| 0 | 0 | 2 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 4 |
| 4 | 0 | 0 | 0 | 0 |
| 0 | 2 | 0 | 0 | 0 |
| 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 4 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 2 |
| 6 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(5,GF(7))| [1,0,0,0,0,0,4,0,0,0,0,0,2,0,0,0,0,0,1,0,0,0,0,0,1],[2,0,0,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,4,0,0,0,0,0,4],[4,0,0,0,0,0,2,0,0,0,0,0,4,0,0,0,0,0,4,0,0,0,0,0,4],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,4,0,0,0,0,0,2],[6,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0] >;
S3×C34 in GAP, Magma, Sage, TeX
S_3\times C_3^4
% in TeX
G:=Group("S3xC3^4"); // GroupNames label
G:=SmallGroup(486,256);
// by ID
G=gap.SmallGroup(486,256);
# by ID
G:=PCGroup([6,-2,-3,-3,-3,-3,-3,11669]);
// 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,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f=e^-1>;
// generators/relations