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## G = C2×S3×C3⋊Dic3order 432 = 24·33

### Direct product of C2, S3 and C3⋊Dic3

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, C335C4, S3×C3×C6, C3×C62, C2×S3×Dic3, C22×C3⋊Dic3, S3×C3⋊Dic3, C6×C3⋊Dic3, C2×C335C4, S3×C62, C2×S3×C3⋊Dic3
Quotients:

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 2A 2B 2C 2D 2E 2F 2G 3A ··· 3E 3F 3G 3H 3I 4A 4B 4C 4D 4E 4F 4G 4H 6A ··· 6O 6P ··· 6AA 6AB ··· 6AQ 12A 12B 12C 12D order 1 2 2 2 2 2 2 2 3 ··· 3 3 3 3 3 4 4 4 4 4 4 4 4 6 ··· 6 6 ··· 6 6 ··· 6 12 12 12 12 size 1 1 1 1 3 3 3 3 2 ··· 2 4 4 4 4 9 9 9 9 27 27 27 27 2 ··· 2 4 ··· 4 6 ··· 6 18 18 18 18

72 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 2 2 2 4 4 4 type + + + + + + + + - + + + - + image C1 C2 C2 C2 C2 C4 S3 S3 D6 Dic3 D6 D6 C4×S3 S32 S3×Dic3 C2×S32 kernel C2×S3×C3⋊Dic3 S3×C3⋊Dic3 C6×C3⋊Dic3 C2×C33⋊5C4 S3×C62 S3×C3×C6 C2×C3⋊Dic3 S3×C2×C6 C3⋊Dic3 S3×C6 S3×C6 C62 C3×C6 C2×C6 C6 C6 # reps 1 4 1 1 1 8 1 4 2 16 8 5 4 4 8 4

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

 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 1 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 12 1 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 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 12 0 0 0 0 0 0 1 12
,
 9 0 0 0 0 0 0 0 4 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 12 0 0 0 0 0 0 1 12
,
 12 8 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 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

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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