G = C3⋊Dic3.2A4 order 432 = 24·33
The non-split extension by C3⋊Dic3 of A4 acting through Inn(C3⋊Dic3)
Aliases: C6.13(S3×A4), C3⋊(Dic3.A4), C3⋊Dic3.2A4, C32⋊4(C4.A4), (Q8×C32).6C6, C12.26D6⋊3C3, (C3×SL2(𝔽3))⋊5S3, SL2(𝔽3)⋊2(C3⋊S3), (C32×SL2(𝔽3))⋊5C2, C2.2(A4×C3⋊S3), Q8.2(C3×C3⋊S3), (C3×C6).18(C2×A4), (C3×Q8).17(C3×S3), SmallGroup(432,625)
Series: Derived ►Chief ►Lower central ►Upper central
| Q8×C32 — C3⋊Dic3.2A4 |
Generators and relations for C3⋊Dic3.2A4
G = < a,b,c,d,e,f | a3=b6=f3=1, c2=d2=e2=b3, ab=ba, cac-1=a-1, ad=da, ae=ea, af=fa, cbc-1=b-1, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, ede-1=b3d, fdf-1=b3de, fef-1=d >
Subgroups: 718 in 114 conjugacy classes, 27 normal (11 characteristic)
C1, C2, C2, C3, C3, C4, C22, S3, C6, C6, C2×C4, D4, Q8, C32, C32, Dic3, C12, D6, C4○D4, C3⋊S3, C3×C6, C3×C6, SL2(𝔽3), SL2(𝔽3), C4×S3, D12, C3×Q8, C33, C3×Dic3, C3⋊Dic3, C3×C12, C2×C3⋊S3, C4.A4, Q8⋊3S3, C32×C6, C3×SL2(𝔽3), C3×SL2(𝔽3), C4×C3⋊S3, C12⋊S3, Q8×C32, C3×C3⋊Dic3, Dic3.A4, C12.26D6, C32×SL2(𝔽3), C3⋊Dic3.2A4
Quotients: C1, C2, C3, S3, C6, A4, C3×S3, C3⋊S3, C2×A4, C4.A4, C3×C3⋊S3, S3×A4, Dic3.A4, A4×C3⋊S3, C3⋊Dic3.2A4
►On 144 points
Generators in S144
(1 28 22)(2 29 23)(3 30 24)(4 25 19)(5 26 20)(6 27 21)(7 16 144)(8 17 139)(9 18 140)(10 13 141)(11 14 142)(12 15 143)(31 37 46)(32 38 47)(33 39 48)(34 40 43)(35 41 44)(36 42 45)(49 55 64)(50 56 65)(51 57 66)(52 58 61)(53 59 62)(54 60 63)(67 79 76)(68 80 77)(69 81 78)(70 82 73)(71 83 74)(72 84 75)(85 97 92)(86 98 93)(87 99 94)(88 100 95)(89 101 96)(90 102 91)(103 115 110)(104 116 111)(105 117 112)(106 118 113)(107 119 114)(108 120 109)(121 133 128)(122 134 129)(123 135 130)(124 136 131)(125 137 132)(126 138 127)
(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 86 4 89)(2 85 5 88)(3 90 6 87)(7 72 10 69)(8 71 11 68)(9 70 12 67)(13 78 16 75)(14 77 17 74)(15 76 18 73)(19 101 22 98)(20 100 23 97)(21 99 24 102)(25 96 28 93)(26 95 29 92)(27 94 30 91)(31 116 34 119)(32 115 35 118)(33 120 36 117)(37 104 40 107)(38 103 41 106)(39 108 42 105)(43 114 46 111)(44 113 47 110)(45 112 48 109)(49 134 52 137)(50 133 53 136)(51 138 54 135)(55 122 58 125)(56 121 59 124)(57 126 60 123)(61 132 64 129)(62 131 65 128)(63 130 66 127)(79 140 82 143)(80 139 83 142)(81 144 84 141)
(1 40 4 37)(2 41 5 38)(3 42 6 39)(7 135 10 138)(8 136 11 133)(9 137 12 134)(13 127 16 130)(14 128 17 131)(15 129 18 132)(19 31 22 34)(20 32 23 35)(21 33 24 36)(25 46 28 43)(26 47 29 44)(27 48 30 45)(49 67 52 70)(50 68 53 71)(51 69 54 72)(55 79 58 82)(56 80 59 83)(57 81 60 84)(61 73 64 76)(62 74 65 77)(63 75 66 78)(85 106 88 103)(86 107 89 104)(87 108 90 105)(91 112 94 109)(92 113 95 110)(93 114 96 111)(97 118 100 115)(98 119 101 116)(99 120 102 117)(121 139 124 142)(122 140 125 143)(123 141 126 144)
(1 58 4 55)(2 59 5 56)(3 60 6 57)(7 120 10 117)(8 115 11 118)(9 116 12 119)(13 112 16 109)(14 113 17 110)(15 114 18 111)(19 49 22 52)(20 50 23 53)(21 51 24 54)(25 64 28 61)(26 65 29 62)(27 66 30 63)(31 70 34 67)(32 71 35 68)(33 72 36 69)(37 82 40 79)(38 83 41 80)(39 84 42 81)(43 76 46 73)(44 77 47 74)(45 78 48 75)(85 124 88 121)(86 125 89 122)(87 126 90 123)(91 130 94 127)(92 131 95 128)(93 132 96 129)(97 136 100 133)(98 137 101 134)(99 138 102 135)(103 142 106 139)(104 143 107 140)(105 144 108 141)
(7 120 138)(8 115 133)(9 116 134)(10 117 135)(11 118 136)(12 119 137)(13 112 130)(14 113 131)(15 114 132)(16 109 127)(17 110 128)(18 111 129)(31 49 67)(32 50 68)(33 51 69)(34 52 70)(35 53 71)(36 54 72)(37 55 79)(38 56 80)(39 57 81)(40 58 82)(41 59 83)(42 60 84)(43 61 73)(44 62 74)(45 63 75)(46 64 76)(47 65 77)(48 66 78)(103 121 139)(104 122 140)(105 123 141)(106 124 142)(107 125 143)(108 126 144)
G:=sub<Sym(144)| (1,28,22)(2,29,23)(3,30,24)(4,25,19)(5,26,20)(6,27,21)(7,16,144)(8,17,139)(9,18,140)(10,13,141)(11,14,142)(12,15,143)(31,37,46)(32,38,47)(33,39,48)(34,40,43)(35,41,44)(36,42,45)(49,55,64)(50,56,65)(51,57,66)(52,58,61)(53,59,62)(54,60,63)(67,79,76)(68,80,77)(69,81,78)(70,82,73)(71,83,74)(72,84,75)(85,97,92)(86,98,93)(87,99,94)(88,100,95)(89,101,96)(90,102,91)(103,115,110)(104,116,111)(105,117,112)(106,118,113)(107,119,114)(108,120,109)(121,133,128)(122,134,129)(123,135,130)(124,136,131)(125,137,132)(126,138,127), (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), (1,86,4,89)(2,85,5,88)(3,90,6,87)(7,72,10,69)(8,71,11,68)(9,70,12,67)(13,78,16,75)(14,77,17,74)(15,76,18,73)(19,101,22,98)(20,100,23,97)(21,99,24,102)(25,96,28,93)(26,95,29,92)(27,94,30,91)(31,116,34,119)(32,115,35,118)(33,120,36,117)(37,104,40,107)(38,103,41,106)(39,108,42,105)(43,114,46,111)(44,113,47,110)(45,112,48,109)(49,134,52,137)(50,133,53,136)(51,138,54,135)(55,122,58,125)(56,121,59,124)(57,126,60,123)(61,132,64,129)(62,131,65,128)(63,130,66,127)(79,140,82,143)(80,139,83,142)(81,144,84,141), (1,40,4,37)(2,41,5,38)(3,42,6,39)(7,135,10,138)(8,136,11,133)(9,137,12,134)(13,127,16,130)(14,128,17,131)(15,129,18,132)(19,31,22,34)(20,32,23,35)(21,33,24,36)(25,46,28,43)(26,47,29,44)(27,48,30,45)(49,67,52,70)(50,68,53,71)(51,69,54,72)(55,79,58,82)(56,80,59,83)(57,81,60,84)(61,73,64,76)(62,74,65,77)(63,75,66,78)(85,106,88,103)(86,107,89,104)(87,108,90,105)(91,112,94,109)(92,113,95,110)(93,114,96,111)(97,118,100,115)(98,119,101,116)(99,120,102,117)(121,139,124,142)(122,140,125,143)(123,141,126,144), (1,58,4,55)(2,59,5,56)(3,60,6,57)(7,120,10,117)(8,115,11,118)(9,116,12,119)(13,112,16,109)(14,113,17,110)(15,114,18,111)(19,49,22,52)(20,50,23,53)(21,51,24,54)(25,64,28,61)(26,65,29,62)(27,66,30,63)(31,70,34,67)(32,71,35,68)(33,72,36,69)(37,82,40,79)(38,83,41,80)(39,84,42,81)(43,76,46,73)(44,77,47,74)(45,78,48,75)(85,124,88,121)(86,125,89,122)(87,126,90,123)(91,130,94,127)(92,131,95,128)(93,132,96,129)(97,136,100,133)(98,137,101,134)(99,138,102,135)(103,142,106,139)(104,143,107,140)(105,144,108,141), (7,120,138)(8,115,133)(9,116,134)(10,117,135)(11,118,136)(12,119,137)(13,112,130)(14,113,131)(15,114,132)(16,109,127)(17,110,128)(18,111,129)(31,49,67)(32,50,68)(33,51,69)(34,52,70)(35,53,71)(36,54,72)(37,55,79)(38,56,80)(39,57,81)(40,58,82)(41,59,83)(42,60,84)(43,61,73)(44,62,74)(45,63,75)(46,64,76)(47,65,77)(48,66,78)(103,121,139)(104,122,140)(105,123,141)(106,124,142)(107,125,143)(108,126,144)>;
G:=Group( (1,28,22)(2,29,23)(3,30,24)(4,25,19)(5,26,20)(6,27,21)(7,16,144)(8,17,139)(9,18,140)(10,13,141)(11,14,142)(12,15,143)(31,37,46)(32,38,47)(33,39,48)(34,40,43)(35,41,44)(36,42,45)(49,55,64)(50,56,65)(51,57,66)(52,58,61)(53,59,62)(54,60,63)(67,79,76)(68,80,77)(69,81,78)(70,82,73)(71,83,74)(72,84,75)(85,97,92)(86,98,93)(87,99,94)(88,100,95)(89,101,96)(90,102,91)(103,115,110)(104,116,111)(105,117,112)(106,118,113)(107,119,114)(108,120,109)(121,133,128)(122,134,129)(123,135,130)(124,136,131)(125,137,132)(126,138,127), (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), (1,86,4,89)(2,85,5,88)(3,90,6,87)(7,72,10,69)(8,71,11,68)(9,70,12,67)(13,78,16,75)(14,77,17,74)(15,76,18,73)(19,101,22,98)(20,100,23,97)(21,99,24,102)(25,96,28,93)(26,95,29,92)(27,94,30,91)(31,116,34,119)(32,115,35,118)(33,120,36,117)(37,104,40,107)(38,103,41,106)(39,108,42,105)(43,114,46,111)(44,113,47,110)(45,112,48,109)(49,134,52,137)(50,133,53,136)(51,138,54,135)(55,122,58,125)(56,121,59,124)(57,126,60,123)(61,132,64,129)(62,131,65,128)(63,130,66,127)(79,140,82,143)(80,139,83,142)(81,144,84,141), (1,40,4,37)(2,41,5,38)(3,42,6,39)(7,135,10,138)(8,136,11,133)(9,137,12,134)(13,127,16,130)(14,128,17,131)(15,129,18,132)(19,31,22,34)(20,32,23,35)(21,33,24,36)(25,46,28,43)(26,47,29,44)(27,48,30,45)(49,67,52,70)(50,68,53,71)(51,69,54,72)(55,79,58,82)(56,80,59,83)(57,81,60,84)(61,73,64,76)(62,74,65,77)(63,75,66,78)(85,106,88,103)(86,107,89,104)(87,108,90,105)(91,112,94,109)(92,113,95,110)(93,114,96,111)(97,118,100,115)(98,119,101,116)(99,120,102,117)(121,139,124,142)(122,140,125,143)(123,141,126,144), (1,58,4,55)(2,59,5,56)(3,60,6,57)(7,120,10,117)(8,115,11,118)(9,116,12,119)(13,112,16,109)(14,113,17,110)(15,114,18,111)(19,49,22,52)(20,50,23,53)(21,51,24,54)(25,64,28,61)(26,65,29,62)(27,66,30,63)(31,70,34,67)(32,71,35,68)(33,72,36,69)(37,82,40,79)(38,83,41,80)(39,84,42,81)(43,76,46,73)(44,77,47,74)(45,78,48,75)(85,124,88,121)(86,125,89,122)(87,126,90,123)(91,130,94,127)(92,131,95,128)(93,132,96,129)(97,136,100,133)(98,137,101,134)(99,138,102,135)(103,142,106,139)(104,143,107,140)(105,144,108,141), (7,120,138)(8,115,133)(9,116,134)(10,117,135)(11,118,136)(12,119,137)(13,112,130)(14,113,131)(15,114,132)(16,109,127)(17,110,128)(18,111,129)(31,49,67)(32,50,68)(33,51,69)(34,52,70)(35,53,71)(36,54,72)(37,55,79)(38,56,80)(39,57,81)(40,58,82)(41,59,83)(42,60,84)(43,61,73)(44,62,74)(45,63,75)(46,64,76)(47,65,77)(48,66,78)(103,121,139)(104,122,140)(105,123,141)(106,124,142)(107,125,143)(108,126,144) );
G=PermutationGroup([[(1,28,22),(2,29,23),(3,30,24),(4,25,19),(5,26,20),(6,27,21),(7,16,144),(8,17,139),(9,18,140),(10,13,141),(11,14,142),(12,15,143),(31,37,46),(32,38,47),(33,39,48),(34,40,43),(35,41,44),(36,42,45),(49,55,64),(50,56,65),(51,57,66),(52,58,61),(53,59,62),(54,60,63),(67,79,76),(68,80,77),(69,81,78),(70,82,73),(71,83,74),(72,84,75),(85,97,92),(86,98,93),(87,99,94),(88,100,95),(89,101,96),(90,102,91),(103,115,110),(104,116,111),(105,117,112),(106,118,113),(107,119,114),(108,120,109),(121,133,128),(122,134,129),(123,135,130),(124,136,131),(125,137,132),(126,138,127)], [(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)], [(1,86,4,89),(2,85,5,88),(3,90,6,87),(7,72,10,69),(8,71,11,68),(9,70,12,67),(13,78,16,75),(14,77,17,74),(15,76,18,73),(19,101,22,98),(20,100,23,97),(21,99,24,102),(25,96,28,93),(26,95,29,92),(27,94,30,91),(31,116,34,119),(32,115,35,118),(33,120,36,117),(37,104,40,107),(38,103,41,106),(39,108,42,105),(43,114,46,111),(44,113,47,110),(45,112,48,109),(49,134,52,137),(50,133,53,136),(51,138,54,135),(55,122,58,125),(56,121,59,124),(57,126,60,123),(61,132,64,129),(62,131,65,128),(63,130,66,127),(79,140,82,143),(80,139,83,142),(81,144,84,141)], [(1,40,4,37),(2,41,5,38),(3,42,6,39),(7,135,10,138),(8,136,11,133),(9,137,12,134),(13,127,16,130),(14,128,17,131),(15,129,18,132),(19,31,22,34),(20,32,23,35),(21,33,24,36),(25,46,28,43),(26,47,29,44),(27,48,30,45),(49,67,52,70),(50,68,53,71),(51,69,54,72),(55,79,58,82),(56,80,59,83),(57,81,60,84),(61,73,64,76),(62,74,65,77),(63,75,66,78),(85,106,88,103),(86,107,89,104),(87,108,90,105),(91,112,94,109),(92,113,95,110),(93,114,96,111),(97,118,100,115),(98,119,101,116),(99,120,102,117),(121,139,124,142),(122,140,125,143),(123,141,126,144)], [(1,58,4,55),(2,59,5,56),(3,60,6,57),(7,120,10,117),(8,115,11,118),(9,116,12,119),(13,112,16,109),(14,113,17,110),(15,114,18,111),(19,49,22,52),(20,50,23,53),(21,51,24,54),(25,64,28,61),(26,65,29,62),(27,66,30,63),(31,70,34,67),(32,71,35,68),(33,72,36,69),(37,82,40,79),(38,83,41,80),(39,84,42,81),(43,76,46,73),(44,77,47,74),(45,78,48,75),(85,124,88,121),(86,125,89,122),(87,126,90,123),(91,130,94,127),(92,131,95,128),(93,132,96,129),(97,136,100,133),(98,137,101,134),(99,138,102,135),(103,142,106,139),(104,143,107,140),(105,144,108,141)], [(7,120,138),(8,115,133),(9,116,134),(10,117,135),(11,118,136),(12,119,137),(13,112,130),(14,113,131),(15,114,132),(16,109,127),(17,110,128),(18,111,129),(31,49,67),(32,50,68),(33,51,69),(34,52,70),(35,53,71),(36,54,72),(37,55,79),(38,56,80),(39,57,81),(40,58,82),(41,59,83),(42,60,84),(43,61,73),(44,62,74),(45,63,75),(46,64,76),(47,65,77),(48,66,78),(103,121,139),(104,122,140),(105,123,141),(106,124,142),(107,125,143),(108,126,144)]])
42 conjugacy classes
| class | 1 | 2A | 2B | 3A | 3B | 3C | 3D | 3E | 3F | 3G | ··· | 3N | 4A | 4B | 4C | 6A | 6B | 6C | 6D | 6E | 6F | 6G | ··· | 6N | 12A | 12B | 12C | 12D | 12E | 12F | 12G | 12H |
| order | 1 | 2 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | ··· | 3 | 4 | 4 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | ··· | 6 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 |
| size | 1 | 1 | 54 | 2 | 2 | 2 | 2 | 4 | 4 | 8 | ··· | 8 | 6 | 9 | 9 | 2 | 2 | 2 | 2 | 4 | 4 | 8 | ··· | 8 | 12 | 12 | 12 | 12 | 36 | 36 | 36 | 36 |
42 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 6 |
| type | + | + | + | + | + | + | + | |||||
| image | C1 | C2 | C3 | C6 | S3 | C3×S3 | C4.A4 | A4 | C2×A4 | Dic3.A4 | Dic3.A4 | S3×A4 |
| kernel | C3⋊Dic3.2A4 | C32×SL2(𝔽3) | C12.26D6 | Q8×C32 | C3×SL2(𝔽3) | C3×Q8 | C32 | C3⋊Dic3 | C3×C6 | C3 | C3 | C6 |
| # reps | 1 | 1 | 2 | 2 | 4 | 8 | 6 | 1 | 1 | 4 | 8 | 4 |
Matrix representation of C3⋊Dic3.2A4 ►in GL6(𝔽13)
| 12 | 1 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 2 |
| 0 | 0 | 0 | 0 | 5 | 11 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 1 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 3 | 3 | 0 | 0 | 0 | 0 |
| 6 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 0 | 0 | 0 |
| 0 | 0 | 0 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 2 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 9 | 0 | 0 |
| 0 | 0 | 9 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 9 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(13))| [12,12,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,5,0,0,0,0,2,11],[0,1,0,0,0,0,12,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[3,6,0,0,0,0,3,10,0,0,0,0,0,0,8,0,0,0,0,0,0,8,0,0,0,0,0,0,1,0,0,0,0,0,2,12],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,12,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,9,0,0,0,0,9,3,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,9,0,0,0,0,0,3,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
C3⋊Dic3.2A4 in GAP, Magma, Sage, TeX
C_3\rtimes {\rm Dic}_3._2A_4 % in TeX
G:=Group("C3:Dic3.2A4"); // GroupNames label
G:=SmallGroup(432,625);
// by ID
G=gap.SmallGroup(432,625);
# by ID
G:=PCGroup([7,-2,-3,-2,2,-3,-3,-2,1512,198,772,94,1081,528,1684,6053]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^3=b^6=f^3=1,c^2=d^2=e^2=b^3,a*b=b*a,c*a*c^-1=a^-1,a*d=d*a,a*e=e*a,a*f=f*a,c*b*c^-1=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,e*d*e^-1=b^3*d,f*d*f^-1=b^3*d*e,f*e*f^-1=d>;
// generators/relations