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G = C2×S3×C3⋊Dic3  order 432 = 24·33

Direct product of C2, S3 and C3⋊Dic3

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

Aliases: C2×S3×C3⋊Dic3, C62.89D6, C6⋊3(S3×Dic3), (S3×C6)⋊3Dic3, (S3×C6).45D6, (S3×C62).5C2, C33⋊12(C22×C4), C33⋊5C4⋊9C22, (C32×C6).52C23, (C3×C62).23C22, C32⋊6(C22×Dic3), (S3×C3×C6)⋊7C4, C6.62(C2×S32), (C2×C6).38S32, C3⋊4(C2×S3×Dic3), (C3×C6)⋊13(C4×S3), (S3×C2×C6).10S3, C32⋊20(S3×C2×C4), C6⋊1(C2×C3⋊Dic3), D6.11(C2×C3⋊S3), (C32×C6)⋊6(C2×C4), (C3×C6)⋊5(C2×Dic3), (S3×C32)⋊7(C2×C4), (C6×C3⋊Dic3)⋊12C2, (C2×C33⋊5C4)⋊5C2, (C3×S3)⋊2(C2×Dic3), C22.11(S3×C3⋊S3), C6.15(C22×C3⋊S3), (S3×C3×C6).29C22, C3⋊1(C22×C3⋊Dic3), (C22×S3).2(C3⋊S3), (C3×C6).146(C22×S3), (C3×C3⋊Dic3)⋊18C22, C2.2(C2×S3×C3⋊S3), (C2×C6).19(C2×C3⋊S3), SmallGroup(432,674)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C33 — C2×S3×C3⋊Dic3
Chief series
C1 — C3 — C32 — C33 — C32×C6 — S3×C3×C6 — S3×C3⋊Dic3 — C2×S3×C3⋊Dic3
Lower central
C33 — C2×S3×C3⋊Dic3
Upper central
C1 — C22

Generators and relations for C2×S3×C3⋊Dic3
 G = < a,b,c,d,e,f | a2=b3=c2=d3=e6=1, f2=e3, ab=ba, ac=ca, ad=da, ae=ea, af=fa, cbc=b-1, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, fdf-1=d-1, fef-1=e-1 >

Subgroups: 1528 in 388 conjugacy classes, 140 normal (18 characteristic)
C1, C2, C2, C2, C3, C3, C3, C4, C22, C22, S3, C6, C6, C6, C2×C4, C23, C32, C32, C32, Dic3, C12, D6, C2×C6, C2×C6, C2×C6, C22×C4, C3×S3, C3×C6, C3×C6, C3×C6, C4×S3, C2×Dic3, C2×C12, C22×S3, C22×C6, C33, C3×Dic3, C3⋊Dic3, C3⋊Dic3, S3×C6, C62, C62, C62, S3×C2×C4, C22×Dic3, S3×C32, C32×C6, C32×C6, S3×Dic3, C6×Dic3, C2×C3⋊Dic3, C2×C3⋊Dic3, S3×C2×C6, C2×C62, C3×C3⋊Dic3, C33⋊5C4, S3×C3×C6, C3×C62, C2×S3×Dic3, C22×C3⋊Dic3, S3×C3⋊Dic3, C6×C3⋊Dic3, C2×C33⋊5C4, S3×C62, C2×S3×C3⋊Dic3
Quotients: C1, C2, C4, C22, S3, C2×C4, C23, Dic3, D6, C22×C4, C3⋊S3, C4×S3, C2×Dic3, C22×S3, C3⋊Dic3, S32, C2×C3⋊S3, S3×C2×C4, C22×Dic3, S3×Dic3, C2×C3⋊Dic3, C2×S32, C22×C3⋊S3, S3×C3⋊S3, C2×S3×Dic3, C22×C3⋊Dic3, S3×C3⋊Dic3, C2×S3×C3⋊S3, C2×S3×C3⋊Dic3

Smallest permutation representation of C2×S3×C3⋊Dic3
►On 144 points
Generators in S144
(1 48)(2 43)(3 44)(4 45)(5 46)(6 47)(7 138)(8 133)(9 134)(10 135)(11 136)(12 137)(13 132)(14 127)(15 128)(16 129)(17 130)(18 131)(19 40)(20 41)(21 42)(22 37)(23 38)(24 39)(25 32)(26 33)(27 34)(28 35)(29 36)(30 31)(49 67)(50 68)(51 69)(52 70)(53 71)(54 72)(55 76)(56 77)(57 78)(58 73)(59 74)(60 75)(61 79)(62 80)(63 81)(64 82)(65 83)(66 84)(85 103)(86 104)(87 105)(88 106)(89 107)(90 108)(91 112)(92 113)(93 114)(94 109)(95 110)(96 111)(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 26 23)(2 27 24)(3 28 19)(4 29 20)(5 30 21)(6 25 22)(7 141 16)(8 142 17)(9 143 18)(10 144 13)(11 139 14)(12 140 15)(31 42 46)(32 37 47)(33 38 48)(34 39 43)(35 40 44)(36 41 45)(49 64 55)(50 65 56)(51 66 57)(52 61 58)(53 62 59)(54 63 60)(67 82 76)(68 83 77)(69 84 78)(70 79 73)(71 80 74)(72 81 75)(85 100 93)(86 101 94)(87 102 95)(88 97 96)(89 98 91)(90 99 92)(103 118 114)(104 119 109)(105 120 110)(106 115 111)(107 116 112)(108 117 113)(121 127 136)(122 128 137)(123 129 138)(124 130 133)(125 131 134)(126 132 135)

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

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

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

72 conjugacy classes

class 1 2A2B2C2D2E2F2G3A···3E3F3G3H3I4A4B4C4D4E4F4G4H6A···6O6P···6AA6AB···6AQ12A12B12C12D
order122222223···33333444444446···66···66···612121212
size111133332···244449999272727272···24···46···618181818

72 irreducible representations

dim1111112222222444
type++++++++-+++-+
imageC1C2C2C2C2C4S3S3D6Dic3D6D6C4×S3S32S3×Dic3C2×S32
kernelC2×S3×C3⋊Dic3S3×C3⋊Dic3C6×C3⋊Dic3C2×C33⋊5C4S3×C62S3×C3×C6C2×C3⋊Dic3S3×C2×C6C3⋊Dic3S3×C6S3×C6C62C3×C6C2×C6C6C6
# reps14111814216854484

Matrix representation of C2×S3×C3⋊Dic3 ►in GL8(𝔽13)

10000000
01000000
001200000
000120000
000012000
000001200
00000010
00000001
,
10000000
01000000
001210000
001200000
000012100
000012000
00000010
00000001
,
10000000
01000000
000120000
001200000
000001200
000012000
00000010
00000001
,
10000000
01000000
00100000
00010000
00001000
00000100
000000012
000000112
,
90000000
43000000
00100000
00010000
000012000
000001200
000000012
000000112
,
128000000
01000000
00100000
00010000
00008000
00000800
00000001
00000010

G:=sub<GL(8,GF(13))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,12,12],[9,4,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,12,12],[12,0,0,0,0,0,0,0,8,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;
 

C2×S3×C3⋊Dic3 in GAP, Magma, Sage, TeX 

C_2\times S_3\times C_3\rtimes {\rm Dic}_3
 
% in TeX
 
G:=Group("C2xS3xC3:Dic3");
 
// GroupNames label
 
G:=SmallGroup(432,674);
 
// by ID
 
G=gap.SmallGroup(432,674);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,64,571,2028,14118]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f|a^2=b^3=c^2=d^3=e^6=1,f^2=e^3,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,c*b*c=b^-1,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^-1=d^-1,f*e*f^-1=e^-1>;
 
// generators/relations
 

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