direct product, metabelian, supersoluble, monomial, A-group
Aliases: C3⋊S3×C22×C6, C63⋊6C2, C62⋊35D6, C33⋊6C24, (C2×C62)⋊13S3, C62⋊21(C2×C6), (C2×C62)⋊14C6, C32⋊8(S3×C23), C32⋊5(C23×C6), (C32×C6)⋊6C23, (C3×C62)⋊18C22, C6⋊2(S3×C2×C6), C3⋊2(S3×C22×C6), (C2×C6)⋊14(S3×C6), (C22×C6)⋊7(C3×S3), (C3×C6)⋊5(C22×C6), (C3×C6)⋊8(C22×S3), SmallGroup(432,773)
Series: Derived ►Chief ►Lower central ►Upper central
| C32 — C3⋊S3×C22×C6 |
Generators and relations for C3⋊S3×C22×C6
G = < a,b,c,d,e,f | a2=b2=c6=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, fdf=d-1, fef=e-1 >
Subgroups: 2692 in 932 conjugacy classes, 294 normal (10 characteristic)
C1, C2, C2, C3, C3, C3, C22, C22, S3, C6, C6, C23, C23, C32, C32, C32, D6, C2×C6, C2×C6, C24, C3×S3, C3⋊S3, C3×C6, C3×C6, C22×S3, C22×C6, C22×C6, C22×C6, C33, S3×C6, C2×C3⋊S3, C62, C62, S3×C23, C23×C6, C3×C3⋊S3, C32×C6, S3×C2×C6, C22×C3⋊S3, C2×C62, C2×C62, C2×C62, C6×C3⋊S3, C3×C62, S3×C22×C6, C23×C3⋊S3, C2×C6×C3⋊S3, C63, C3⋊S3×C22×C6
Quotients: C1, C2, C3, C22, S3, C6, C23, D6, C2×C6, C24, C3×S3, C3⋊S3, C22×S3, C22×C6, S3×C6, C2×C3⋊S3, S3×C23, C23×C6, C3×C3⋊S3, S3×C2×C6, C22×C3⋊S3, C6×C3⋊S3, S3×C22×C6, C23×C3⋊S3, C2×C6×C3⋊S3, C3⋊S3×C22×C6
►On 144 points
Generators in S144
(1 67)(2 68)(3 69)(4 70)(5 71)(6 72)(7 101)(8 102)(9 97)(10 98)(11 99)(12 100)(13 93)(14 94)(15 95)(16 96)(17 91)(18 92)(19 76)(20 77)(21 78)(22 73)(23 74)(24 75)(25 82)(26 83)(27 84)(28 79)(29 80)(30 81)(31 52)(32 53)(33 54)(34 49)(35 50)(36 51)(37 58)(38 59)(39 60)(40 55)(41 56)(42 57)(43 64)(44 65)(45 66)(46 61)(47 62)(48 63)(85 142)(86 143)(87 144)(88 139)(89 140)(90 141)(103 124)(104 125)(105 126)(106 121)(107 122)(108 123)(109 130)(110 131)(111 132)(112 127)(113 128)(114 129)(115 136)(116 137)(117 138)(118 133)(119 134)(120 135)
(1 34)(2 35)(3 36)(4 31)(5 32)(6 33)(7 134)(8 135)(9 136)(10 137)(11 138)(12 133)(13 132)(14 127)(15 128)(16 129)(17 130)(18 131)(19 37)(20 38)(21 39)(22 40)(23 41)(24 42)(25 43)(26 44)(27 45)(28 46)(29 47)(30 48)(49 67)(50 68)(51 69)(52 70)(53 71)(54 72)(55 73)(56 74)(57 75)(58 76)(59 77)(60 78)(61 79)(62 80)(63 81)(64 82)(65 83)(66 84)(85 103)(86 104)(87 105)(88 106)(89 107)(90 108)(91 109)(92 110)(93 111)(94 112)(95 113)(96 114)(97 115)(98 116)(99 117)(100 118)(101 119)(102 120)(121 139)(122 140)(123 141)(124 142)(125 143)(126 144)
(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)
(1 26 21)(2 27 22)(3 28 23)(4 29 24)(5 30 19)(6 25 20)(7 142 16)(8 143 17)(9 144 18)(10 139 13)(11 140 14)(12 141 15)(31 47 42)(32 48 37)(33 43 38)(34 44 39)(35 45 40)(36 46 41)(49 65 60)(50 66 55)(51 61 56)(52 62 57)(53 63 58)(54 64 59)(67 83 78)(68 84 73)(69 79 74)(70 80 75)(71 81 76)(72 82 77)(85 96 101)(86 91 102)(87 92 97)(88 93 98)(89 94 99)(90 95 100)(103 114 119)(104 109 120)(105 110 115)(106 111 116)(107 112 117)(108 113 118)(121 132 137)(122 127 138)(123 128 133)(124 129 134)(125 130 135)(126 131 136)
(1 23 30)(2 24 25)(3 19 26)(4 20 27)(5 21 28)(6 22 29)(7 14 144)(8 15 139)(9 16 140)(10 17 141)(11 18 142)(12 13 143)(31 38 45)(32 39 46)(33 40 47)(34 41 48)(35 42 43)(36 37 44)(49 56 63)(50 57 64)(51 58 65)(52 59 66)(53 60 61)(54 55 62)(67 74 81)(68 75 82)(69 76 83)(70 77 84)(71 78 79)(72 73 80)(85 99 92)(86 100 93)(87 101 94)(88 102 95)(89 97 96)(90 98 91)(103 117 110)(104 118 111)(105 119 112)(106 120 113)(107 115 114)(108 116 109)(121 135 128)(122 136 129)(123 137 130)(124 138 131)(125 133 132)(126 134 127)
(1 88)(2 89)(3 90)(4 85)(5 86)(6 87)(7 80)(8 81)(9 82)(10 83)(11 84)(12 79)(13 78)(14 73)(15 74)(16 75)(17 76)(18 77)(19 91)(20 92)(21 93)(22 94)(23 95)(24 96)(25 97)(26 98)(27 99)(28 100)(29 101)(30 102)(31 103)(32 104)(33 105)(34 106)(35 107)(36 108)(37 109)(38 110)(39 111)(40 112)(41 113)(42 114)(43 115)(44 116)(45 117)(46 118)(47 119)(48 120)(49 121)(50 122)(51 123)(52 124)(53 125)(54 126)(55 127)(56 128)(57 129)(58 130)(59 131)(60 132)(61 133)(62 134)(63 135)(64 136)(65 137)(66 138)(67 139)(68 140)(69 141)(70 142)(71 143)(72 144)
G:=sub<Sym(144)| (1,67)(2,68)(3,69)(4,70)(5,71)(6,72)(7,101)(8,102)(9,97)(10,98)(11,99)(12,100)(13,93)(14,94)(15,95)(16,96)(17,91)(18,92)(19,76)(20,77)(21,78)(22,73)(23,74)(24,75)(25,82)(26,83)(27,84)(28,79)(29,80)(30,81)(31,52)(32,53)(33,54)(34,49)(35,50)(36,51)(37,58)(38,59)(39,60)(40,55)(41,56)(42,57)(43,64)(44,65)(45,66)(46,61)(47,62)(48,63)(85,142)(86,143)(87,144)(88,139)(89,140)(90,141)(103,124)(104,125)(105,126)(106,121)(107,122)(108,123)(109,130)(110,131)(111,132)(112,127)(113,128)(114,129)(115,136)(116,137)(117,138)(118,133)(119,134)(120,135), (1,34)(2,35)(3,36)(4,31)(5,32)(6,33)(7,134)(8,135)(9,136)(10,137)(11,138)(12,133)(13,132)(14,127)(15,128)(16,129)(17,130)(18,131)(19,37)(20,38)(21,39)(22,40)(23,41)(24,42)(25,43)(26,44)(27,45)(28,46)(29,47)(30,48)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(55,73)(56,74)(57,75)(58,76)(59,77)(60,78)(61,79)(62,80)(63,81)(64,82)(65,83)(66,84)(85,103)(86,104)(87,105)(88,106)(89,107)(90,108)(91,109)(92,110)(93,111)(94,112)(95,113)(96,114)(97,115)(98,116)(99,117)(100,118)(101,119)(102,120)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144), (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), (1,26,21)(2,27,22)(3,28,23)(4,29,24)(5,30,19)(6,25,20)(7,142,16)(8,143,17)(9,144,18)(10,139,13)(11,140,14)(12,141,15)(31,47,42)(32,48,37)(33,43,38)(34,44,39)(35,45,40)(36,46,41)(49,65,60)(50,66,55)(51,61,56)(52,62,57)(53,63,58)(54,64,59)(67,83,78)(68,84,73)(69,79,74)(70,80,75)(71,81,76)(72,82,77)(85,96,101)(86,91,102)(87,92,97)(88,93,98)(89,94,99)(90,95,100)(103,114,119)(104,109,120)(105,110,115)(106,111,116)(107,112,117)(108,113,118)(121,132,137)(122,127,138)(123,128,133)(124,129,134)(125,130,135)(126,131,136), (1,23,30)(2,24,25)(3,19,26)(4,20,27)(5,21,28)(6,22,29)(7,14,144)(8,15,139)(9,16,140)(10,17,141)(11,18,142)(12,13,143)(31,38,45)(32,39,46)(33,40,47)(34,41,48)(35,42,43)(36,37,44)(49,56,63)(50,57,64)(51,58,65)(52,59,66)(53,60,61)(54,55,62)(67,74,81)(68,75,82)(69,76,83)(70,77,84)(71,78,79)(72,73,80)(85,99,92)(86,100,93)(87,101,94)(88,102,95)(89,97,96)(90,98,91)(103,117,110)(104,118,111)(105,119,112)(106,120,113)(107,115,114)(108,116,109)(121,135,128)(122,136,129)(123,137,130)(124,138,131)(125,133,132)(126,134,127), (1,88)(2,89)(3,90)(4,85)(5,86)(6,87)(7,80)(8,81)(9,82)(10,83)(11,84)(12,79)(13,78)(14,73)(15,74)(16,75)(17,76)(18,77)(19,91)(20,92)(21,93)(22,94)(23,95)(24,96)(25,97)(26,98)(27,99)(28,100)(29,101)(30,102)(31,103)(32,104)(33,105)(34,106)(35,107)(36,108)(37,109)(38,110)(39,111)(40,112)(41,113)(42,114)(43,115)(44,116)(45,117)(46,118)(47,119)(48,120)(49,121)(50,122)(51,123)(52,124)(53,125)(54,126)(55,127)(56,128)(57,129)(58,130)(59,131)(60,132)(61,133)(62,134)(63,135)(64,136)(65,137)(66,138)(67,139)(68,140)(69,141)(70,142)(71,143)(72,144)>;
G:=Group( (1,67)(2,68)(3,69)(4,70)(5,71)(6,72)(7,101)(8,102)(9,97)(10,98)(11,99)(12,100)(13,93)(14,94)(15,95)(16,96)(17,91)(18,92)(19,76)(20,77)(21,78)(22,73)(23,74)(24,75)(25,82)(26,83)(27,84)(28,79)(29,80)(30,81)(31,52)(32,53)(33,54)(34,49)(35,50)(36,51)(37,58)(38,59)(39,60)(40,55)(41,56)(42,57)(43,64)(44,65)(45,66)(46,61)(47,62)(48,63)(85,142)(86,143)(87,144)(88,139)(89,140)(90,141)(103,124)(104,125)(105,126)(106,121)(107,122)(108,123)(109,130)(110,131)(111,132)(112,127)(113,128)(114,129)(115,136)(116,137)(117,138)(118,133)(119,134)(120,135), (1,34)(2,35)(3,36)(4,31)(5,32)(6,33)(7,134)(8,135)(9,136)(10,137)(11,138)(12,133)(13,132)(14,127)(15,128)(16,129)(17,130)(18,131)(19,37)(20,38)(21,39)(22,40)(23,41)(24,42)(25,43)(26,44)(27,45)(28,46)(29,47)(30,48)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(55,73)(56,74)(57,75)(58,76)(59,77)(60,78)(61,79)(62,80)(63,81)(64,82)(65,83)(66,84)(85,103)(86,104)(87,105)(88,106)(89,107)(90,108)(91,109)(92,110)(93,111)(94,112)(95,113)(96,114)(97,115)(98,116)(99,117)(100,118)(101,119)(102,120)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144), (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), (1,26,21)(2,27,22)(3,28,23)(4,29,24)(5,30,19)(6,25,20)(7,142,16)(8,143,17)(9,144,18)(10,139,13)(11,140,14)(12,141,15)(31,47,42)(32,48,37)(33,43,38)(34,44,39)(35,45,40)(36,46,41)(49,65,60)(50,66,55)(51,61,56)(52,62,57)(53,63,58)(54,64,59)(67,83,78)(68,84,73)(69,79,74)(70,80,75)(71,81,76)(72,82,77)(85,96,101)(86,91,102)(87,92,97)(88,93,98)(89,94,99)(90,95,100)(103,114,119)(104,109,120)(105,110,115)(106,111,116)(107,112,117)(108,113,118)(121,132,137)(122,127,138)(123,128,133)(124,129,134)(125,130,135)(126,131,136), (1,23,30)(2,24,25)(3,19,26)(4,20,27)(5,21,28)(6,22,29)(7,14,144)(8,15,139)(9,16,140)(10,17,141)(11,18,142)(12,13,143)(31,38,45)(32,39,46)(33,40,47)(34,41,48)(35,42,43)(36,37,44)(49,56,63)(50,57,64)(51,58,65)(52,59,66)(53,60,61)(54,55,62)(67,74,81)(68,75,82)(69,76,83)(70,77,84)(71,78,79)(72,73,80)(85,99,92)(86,100,93)(87,101,94)(88,102,95)(89,97,96)(90,98,91)(103,117,110)(104,118,111)(105,119,112)(106,120,113)(107,115,114)(108,116,109)(121,135,128)(122,136,129)(123,137,130)(124,138,131)(125,133,132)(126,134,127), (1,88)(2,89)(3,90)(4,85)(5,86)(6,87)(7,80)(8,81)(9,82)(10,83)(11,84)(12,79)(13,78)(14,73)(15,74)(16,75)(17,76)(18,77)(19,91)(20,92)(21,93)(22,94)(23,95)(24,96)(25,97)(26,98)(27,99)(28,100)(29,101)(30,102)(31,103)(32,104)(33,105)(34,106)(35,107)(36,108)(37,109)(38,110)(39,111)(40,112)(41,113)(42,114)(43,115)(44,116)(45,117)(46,118)(47,119)(48,120)(49,121)(50,122)(51,123)(52,124)(53,125)(54,126)(55,127)(56,128)(57,129)(58,130)(59,131)(60,132)(61,133)(62,134)(63,135)(64,136)(65,137)(66,138)(67,139)(68,140)(69,141)(70,142)(71,143)(72,144) );
G=PermutationGroup([[(1,67),(2,68),(3,69),(4,70),(5,71),(6,72),(7,101),(8,102),(9,97),(10,98),(11,99),(12,100),(13,93),(14,94),(15,95),(16,96),(17,91),(18,92),(19,76),(20,77),(21,78),(22,73),(23,74),(24,75),(25,82),(26,83),(27,84),(28,79),(29,80),(30,81),(31,52),(32,53),(33,54),(34,49),(35,50),(36,51),(37,58),(38,59),(39,60),(40,55),(41,56),(42,57),(43,64),(44,65),(45,66),(46,61),(47,62),(48,63),(85,142),(86,143),(87,144),(88,139),(89,140),(90,141),(103,124),(104,125),(105,126),(106,121),(107,122),(108,123),(109,130),(110,131),(111,132),(112,127),(113,128),(114,129),(115,136),(116,137),(117,138),(118,133),(119,134),(120,135)], [(1,34),(2,35),(3,36),(4,31),(5,32),(6,33),(7,134),(8,135),(9,136),(10,137),(11,138),(12,133),(13,132),(14,127),(15,128),(16,129),(17,130),(18,131),(19,37),(20,38),(21,39),(22,40),(23,41),(24,42),(25,43),(26,44),(27,45),(28,46),(29,47),(30,48),(49,67),(50,68),(51,69),(52,70),(53,71),(54,72),(55,73),(56,74),(57,75),(58,76),(59,77),(60,78),(61,79),(62,80),(63,81),(64,82),(65,83),(66,84),(85,103),(86,104),(87,105),(88,106),(89,107),(90,108),(91,109),(92,110),(93,111),(94,112),(95,113),(96,114),(97,115),(98,116),(99,117),(100,118),(101,119),(102,120),(121,139),(122,140),(123,141),(124,142),(125,143),(126,144)], [(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)], [(1,26,21),(2,27,22),(3,28,23),(4,29,24),(5,30,19),(6,25,20),(7,142,16),(8,143,17),(9,144,18),(10,139,13),(11,140,14),(12,141,15),(31,47,42),(32,48,37),(33,43,38),(34,44,39),(35,45,40),(36,46,41),(49,65,60),(50,66,55),(51,61,56),(52,62,57),(53,63,58),(54,64,59),(67,83,78),(68,84,73),(69,79,74),(70,80,75),(71,81,76),(72,82,77),(85,96,101),(86,91,102),(87,92,97),(88,93,98),(89,94,99),(90,95,100),(103,114,119),(104,109,120),(105,110,115),(106,111,116),(107,112,117),(108,113,118),(121,132,137),(122,127,138),(123,128,133),(124,129,134),(125,130,135),(126,131,136)], [(1,23,30),(2,24,25),(3,19,26),(4,20,27),(5,21,28),(6,22,29),(7,14,144),(8,15,139),(9,16,140),(10,17,141),(11,18,142),(12,13,143),(31,38,45),(32,39,46),(33,40,47),(34,41,48),(35,42,43),(36,37,44),(49,56,63),(50,57,64),(51,58,65),(52,59,66),(53,60,61),(54,55,62),(67,74,81),(68,75,82),(69,76,83),(70,77,84),(71,78,79),(72,73,80),(85,99,92),(86,100,93),(87,101,94),(88,102,95),(89,97,96),(90,98,91),(103,117,110),(104,118,111),(105,119,112),(106,120,113),(107,115,114),(108,116,109),(121,135,128),(122,136,129),(123,137,130),(124,138,131),(125,133,132),(126,134,127)], [(1,88),(2,89),(3,90),(4,85),(5,86),(6,87),(7,80),(8,81),(9,82),(10,83),(11,84),(12,79),(13,78),(14,73),(15,74),(16,75),(17,76),(18,77),(19,91),(20,92),(21,93),(22,94),(23,95),(24,96),(25,97),(26,98),(27,99),(28,100),(29,101),(30,102),(31,103),(32,104),(33,105),(34,106),(35,107),(36,108),(37,109),(38,110),(39,111),(40,112),(41,113),(42,114),(43,115),(44,116),(45,117),(46,118),(47,119),(48,120),(49,121),(50,122),(51,123),(52,124),(53,125),(54,126),(55,127),(56,128),(57,129),(58,130),(59,131),(60,132),(61,133),(62,134),(63,135),(64,136),(65,137),(66,138),(67,139),(68,140),(69,141),(70,142),(71,143),(72,144)]])
144 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | ··· | 2O | 3A | 3B | 3C | ··· | 3N | 6A | ··· | 6N | 6O | ··· | 6CT | 6CU | ··· | 6DJ |
| order | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 3 | 3 | 3 | ··· | 3 | 6 | ··· | 6 | 6 | ··· | 6 | 6 | ··· | 6 |
| size | 1 | 1 | ··· | 1 | 9 | ··· | 9 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 9 | ··· | 9 |
144 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | |||||
| image | C1 | C2 | C2 | C3 | C6 | C6 | S3 | D6 | C3×S3 | S3×C6 |
| kernel | C3⋊S3×C22×C6 | C2×C6×C3⋊S3 | C63 | C23×C3⋊S3 | C22×C3⋊S3 | C2×C62 | C2×C62 | C62 | C22×C6 | C2×C6 |
| # reps | 1 | 14 | 1 | 2 | 28 | 2 | 4 | 28 | 8 | 56 |
Matrix representation of C3⋊S3×C22×C6 ►in GL5(𝔽7)
| 6 | 0 | 0 | 0 | 0 |
| 0 | 6 | 0 | 0 | 0 |
| 0 | 0 | 6 | 0 | 0 |
| 0 | 0 | 0 | 6 | 0 |
| 0 | 0 | 0 | 0 | 6 |
| 6 | 0 | 0 | 0 | 0 |
| 0 | 6 | 0 | 0 | 0 |
| 0 | 0 | 6 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 2 | 0 | 0 | 0 | 0 |
| 0 | 3 | 0 | 0 | 0 |
| 0 | 0 | 3 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 4 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 2 | 0 | 0 | 0 |
| 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 2 |
| 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 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 0 | 0 |
| 0 | 4 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(5,GF(7))| [6,0,0,0,0,0,6,0,0,0,0,0,6,0,0,0,0,0,6,0,0,0,0,0,6],[6,0,0,0,0,0,6,0,0,0,0,0,6,0,0,0,0,0,1,0,0,0,0,0,1],[2,0,0,0,0,0,3,0,0,0,0,0,3,0,0,0,0,0,4,0,0,0,0,0,4],[1,0,0,0,0,0,2,0,0,0,0,0,4,0,0,0,0,0,4,0,0,0,0,0,2],[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],[1,0,0,0,0,0,0,4,0,0,0,2,0,0,0,0,0,0,0,1,0,0,0,1,0] >;
C3⋊S3×C22×C6 in GAP, Magma, Sage, TeX
C_3\rtimes S_3\times C_2^2\times C_6
% in TeX
G:=Group("C3:S3xC2^2xC6"); // GroupNames label
G:=SmallGroup(432,773);
// by ID
G=gap.SmallGroup(432,773);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,4037,14118]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^6=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,f*d*f=d^-1,f*e*f=e^-1>;
// generators/relations