direct product, metabelian, supersoluble, monomial, A-group
Aliases: S3×C32⋊4C8, C12.67S32, C33⋊10(C2×C8), (S3×C32)⋊4C8, C32⋊15(S3×C8), C33⋊7C8⋊7C2, (S3×C12).12S3, (C3×C12).182D6, (S3×C6).6Dic3, C6.28(S3×Dic3), D6.2(C3⋊Dic3), (C3×Dic3).6Dic3, (C32×Dic3).6C4, Dic3.2(C3⋊Dic3), (C32×C12).64C22, C3⋊3(S3×C3⋊C8), (C3×S3)⋊(C3⋊C8), (S3×C3×C6).5C4, C32⋊6(C2×C3⋊C8), C4.22(S3×C3⋊S3), (S3×C3×C12).7C2, C12.37(C2×C3⋊S3), (C3×C6).89(C4×S3), C3⋊1(C2×C32⋊4C8), C6.1(C2×C3⋊Dic3), C2.1(S3×C3⋊Dic3), (C4×S3).3(C3⋊S3), (C3×C32⋊4C8)⋊9C2, (C32×C6).31(C2×C4), (C3×C6).35(C2×Dic3), SmallGroup(432,430)
Series: Derived ►Chief ►Lower central ►Upper central
| C33 — S3×C32⋊4C8 |
Generators and relations for S3×C32⋊4C8
G = < a,b,c,d,e | a3=b2=c3=d3=e8=1, bab=a-1, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ece-1=c-1, ede-1=d-1 >
Subgroups: 520 in 164 conjugacy classes, 70 normal (22 characteristic)
C1, C2, C2, C3, C3, C3, C4, C4, C22, S3, C6, C6, C6, C8, C2×C4, C32, C32, C32, Dic3, C12, C12, C12, D6, C2×C6, C2×C8, C3×S3, C3×C6, C3×C6, C3×C6, C3⋊C8, C24, C4×S3, C2×C12, C33, C3×Dic3, C3×C12, C3×C12, C3×C12, S3×C6, C62, S3×C8, C2×C3⋊C8, S3×C32, C32×C6, C3×C3⋊C8, C32⋊4C8, C32⋊4C8, S3×C12, C6×C12, C32×Dic3, C32×C12, S3×C3×C6, S3×C3⋊C8, C2×C32⋊4C8, C3×C32⋊4C8, C33⋊7C8, S3×C3×C12, S3×C32⋊4C8
Quotients: C1, C2, C4, C22, S3, C8, C2×C4, Dic3, D6, C2×C8, C3⋊S3, C3⋊C8, C4×S3, C2×Dic3, C3⋊Dic3, S32, C2×C3⋊S3, S3×C8, C2×C3⋊C8, C32⋊4C8, S3×Dic3, C2×C3⋊Dic3, S3×C3⋊S3, S3×C3⋊C8, C2×C32⋊4C8, S3×C3⋊Dic3, S3×C32⋊4C8
►On 144 points
Generators in S144
(1 120 95)(2 113 96)(3 114 89)(4 115 90)(5 116 91)(6 117 92)(7 118 93)(8 119 94)(9 40 44)(10 33 45)(11 34 46)(12 35 47)(13 36 48)(14 37 41)(15 38 42)(16 39 43)(17 32 55)(18 25 56)(19 26 49)(20 27 50)(21 28 51)(22 29 52)(23 30 53)(24 31 54)(57 110 142)(58 111 143)(59 112 144)(60 105 137)(61 106 138)(62 107 139)(63 108 140)(64 109 141)(65 122 103)(66 123 104)(67 124 97)(68 125 98)(69 126 99)(70 127 100)(71 128 101)(72 121 102)(73 88 131)(74 81 132)(75 82 133)(76 83 134)(77 84 135)(78 85 136)(79 86 129)(80 87 130)
(1 54)(2 55)(3 56)(4 49)(5 50)(6 51)(7 52)(8 53)(9 80)(10 73)(11 74)(12 75)(13 76)(14 77)(15 78)(16 79)(17 96)(18 89)(19 90)(20 91)(21 92)(22 93)(23 94)(24 95)(25 114)(26 115)(27 116)(28 117)(29 118)(30 119)(31 120)(32 113)(33 131)(34 132)(35 133)(36 134)(37 135)(38 136)(39 129)(40 130)(41 84)(42 85)(43 86)(44 87)(45 88)(46 81)(47 82)(48 83)(57 100)(58 101)(59 102)(60 103)(61 104)(62 97)(63 98)(64 99)(65 137)(66 138)(67 139)(68 140)(69 141)(70 142)(71 143)(72 144)(105 122)(106 123)(107 124)(108 125)(109 126)(110 127)(111 128)(112 121)
(1 125 75)(2 76 126)(3 127 77)(4 78 128)(5 121 79)(6 80 122)(7 123 73)(8 74 124)(9 105 51)(10 52 106)(11 107 53)(12 54 108)(13 109 55)(14 56 110)(15 111 49)(16 50 112)(17 36 141)(18 142 37)(19 38 143)(20 144 39)(21 40 137)(22 138 33)(23 34 139)(24 140 35)(25 57 41)(26 42 58)(27 59 43)(28 44 60)(29 61 45)(30 46 62)(31 63 47)(32 48 64)(65 92 130)(66 131 93)(67 94 132)(68 133 95)(69 96 134)(70 135 89)(71 90 136)(72 129 91)(81 97 119)(82 120 98)(83 99 113)(84 114 100)(85 101 115)(86 116 102)(87 103 117)(88 118 104)
(1 68 82)(2 83 69)(3 70 84)(4 85 71)(5 72 86)(6 87 65)(7 66 88)(8 81 67)(9 60 21)(10 22 61)(11 62 23)(12 24 63)(13 64 17)(14 18 57)(15 58 19)(16 20 59)(25 110 37)(26 38 111)(27 112 39)(28 40 105)(29 106 33)(30 34 107)(31 108 35)(32 36 109)(41 56 142)(42 143 49)(43 50 144)(44 137 51)(45 52 138)(46 139 53)(47 54 140)(48 141 55)(73 93 104)(74 97 94)(75 95 98)(76 99 96)(77 89 100)(78 101 90)(79 91 102)(80 103 92)(113 134 126)(114 127 135)(115 136 128)(116 121 129)(117 130 122)(118 123 131)(119 132 124)(120 125 133)
(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)
G:=sub<Sym(144)| (1,120,95)(2,113,96)(3,114,89)(4,115,90)(5,116,91)(6,117,92)(7,118,93)(8,119,94)(9,40,44)(10,33,45)(11,34,46)(12,35,47)(13,36,48)(14,37,41)(15,38,42)(16,39,43)(17,32,55)(18,25,56)(19,26,49)(20,27,50)(21,28,51)(22,29,52)(23,30,53)(24,31,54)(57,110,142)(58,111,143)(59,112,144)(60,105,137)(61,106,138)(62,107,139)(63,108,140)(64,109,141)(65,122,103)(66,123,104)(67,124,97)(68,125,98)(69,126,99)(70,127,100)(71,128,101)(72,121,102)(73,88,131)(74,81,132)(75,82,133)(76,83,134)(77,84,135)(78,85,136)(79,86,129)(80,87,130), (1,54)(2,55)(3,56)(4,49)(5,50)(6,51)(7,52)(8,53)(9,80)(10,73)(11,74)(12,75)(13,76)(14,77)(15,78)(16,79)(17,96)(18,89)(19,90)(20,91)(21,92)(22,93)(23,94)(24,95)(25,114)(26,115)(27,116)(28,117)(29,118)(30,119)(31,120)(32,113)(33,131)(34,132)(35,133)(36,134)(37,135)(38,136)(39,129)(40,130)(41,84)(42,85)(43,86)(44,87)(45,88)(46,81)(47,82)(48,83)(57,100)(58,101)(59,102)(60,103)(61,104)(62,97)(63,98)(64,99)(65,137)(66,138)(67,139)(68,140)(69,141)(70,142)(71,143)(72,144)(105,122)(106,123)(107,124)(108,125)(109,126)(110,127)(111,128)(112,121), (1,125,75)(2,76,126)(3,127,77)(4,78,128)(5,121,79)(6,80,122)(7,123,73)(8,74,124)(9,105,51)(10,52,106)(11,107,53)(12,54,108)(13,109,55)(14,56,110)(15,111,49)(16,50,112)(17,36,141)(18,142,37)(19,38,143)(20,144,39)(21,40,137)(22,138,33)(23,34,139)(24,140,35)(25,57,41)(26,42,58)(27,59,43)(28,44,60)(29,61,45)(30,46,62)(31,63,47)(32,48,64)(65,92,130)(66,131,93)(67,94,132)(68,133,95)(69,96,134)(70,135,89)(71,90,136)(72,129,91)(81,97,119)(82,120,98)(83,99,113)(84,114,100)(85,101,115)(86,116,102)(87,103,117)(88,118,104), (1,68,82)(2,83,69)(3,70,84)(4,85,71)(5,72,86)(6,87,65)(7,66,88)(8,81,67)(9,60,21)(10,22,61)(11,62,23)(12,24,63)(13,64,17)(14,18,57)(15,58,19)(16,20,59)(25,110,37)(26,38,111)(27,112,39)(28,40,105)(29,106,33)(30,34,107)(31,108,35)(32,36,109)(41,56,142)(42,143,49)(43,50,144)(44,137,51)(45,52,138)(46,139,53)(47,54,140)(48,141,55)(73,93,104)(74,97,94)(75,95,98)(76,99,96)(77,89,100)(78,101,90)(79,91,102)(80,103,92)(113,134,126)(114,127,135)(115,136,128)(116,121,129)(117,130,122)(118,123,131)(119,132,124)(120,125,133), (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)>;
G:=Group( (1,120,95)(2,113,96)(3,114,89)(4,115,90)(5,116,91)(6,117,92)(7,118,93)(8,119,94)(9,40,44)(10,33,45)(11,34,46)(12,35,47)(13,36,48)(14,37,41)(15,38,42)(16,39,43)(17,32,55)(18,25,56)(19,26,49)(20,27,50)(21,28,51)(22,29,52)(23,30,53)(24,31,54)(57,110,142)(58,111,143)(59,112,144)(60,105,137)(61,106,138)(62,107,139)(63,108,140)(64,109,141)(65,122,103)(66,123,104)(67,124,97)(68,125,98)(69,126,99)(70,127,100)(71,128,101)(72,121,102)(73,88,131)(74,81,132)(75,82,133)(76,83,134)(77,84,135)(78,85,136)(79,86,129)(80,87,130), (1,54)(2,55)(3,56)(4,49)(5,50)(6,51)(7,52)(8,53)(9,80)(10,73)(11,74)(12,75)(13,76)(14,77)(15,78)(16,79)(17,96)(18,89)(19,90)(20,91)(21,92)(22,93)(23,94)(24,95)(25,114)(26,115)(27,116)(28,117)(29,118)(30,119)(31,120)(32,113)(33,131)(34,132)(35,133)(36,134)(37,135)(38,136)(39,129)(40,130)(41,84)(42,85)(43,86)(44,87)(45,88)(46,81)(47,82)(48,83)(57,100)(58,101)(59,102)(60,103)(61,104)(62,97)(63,98)(64,99)(65,137)(66,138)(67,139)(68,140)(69,141)(70,142)(71,143)(72,144)(105,122)(106,123)(107,124)(108,125)(109,126)(110,127)(111,128)(112,121), (1,125,75)(2,76,126)(3,127,77)(4,78,128)(5,121,79)(6,80,122)(7,123,73)(8,74,124)(9,105,51)(10,52,106)(11,107,53)(12,54,108)(13,109,55)(14,56,110)(15,111,49)(16,50,112)(17,36,141)(18,142,37)(19,38,143)(20,144,39)(21,40,137)(22,138,33)(23,34,139)(24,140,35)(25,57,41)(26,42,58)(27,59,43)(28,44,60)(29,61,45)(30,46,62)(31,63,47)(32,48,64)(65,92,130)(66,131,93)(67,94,132)(68,133,95)(69,96,134)(70,135,89)(71,90,136)(72,129,91)(81,97,119)(82,120,98)(83,99,113)(84,114,100)(85,101,115)(86,116,102)(87,103,117)(88,118,104), (1,68,82)(2,83,69)(3,70,84)(4,85,71)(5,72,86)(6,87,65)(7,66,88)(8,81,67)(9,60,21)(10,22,61)(11,62,23)(12,24,63)(13,64,17)(14,18,57)(15,58,19)(16,20,59)(25,110,37)(26,38,111)(27,112,39)(28,40,105)(29,106,33)(30,34,107)(31,108,35)(32,36,109)(41,56,142)(42,143,49)(43,50,144)(44,137,51)(45,52,138)(46,139,53)(47,54,140)(48,141,55)(73,93,104)(74,97,94)(75,95,98)(76,99,96)(77,89,100)(78,101,90)(79,91,102)(80,103,92)(113,134,126)(114,127,135)(115,136,128)(116,121,129)(117,130,122)(118,123,131)(119,132,124)(120,125,133), (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) );
G=PermutationGroup([[(1,120,95),(2,113,96),(3,114,89),(4,115,90),(5,116,91),(6,117,92),(7,118,93),(8,119,94),(9,40,44),(10,33,45),(11,34,46),(12,35,47),(13,36,48),(14,37,41),(15,38,42),(16,39,43),(17,32,55),(18,25,56),(19,26,49),(20,27,50),(21,28,51),(22,29,52),(23,30,53),(24,31,54),(57,110,142),(58,111,143),(59,112,144),(60,105,137),(61,106,138),(62,107,139),(63,108,140),(64,109,141),(65,122,103),(66,123,104),(67,124,97),(68,125,98),(69,126,99),(70,127,100),(71,128,101),(72,121,102),(73,88,131),(74,81,132),(75,82,133),(76,83,134),(77,84,135),(78,85,136),(79,86,129),(80,87,130)], [(1,54),(2,55),(3,56),(4,49),(5,50),(6,51),(7,52),(8,53),(9,80),(10,73),(11,74),(12,75),(13,76),(14,77),(15,78),(16,79),(17,96),(18,89),(19,90),(20,91),(21,92),(22,93),(23,94),(24,95),(25,114),(26,115),(27,116),(28,117),(29,118),(30,119),(31,120),(32,113),(33,131),(34,132),(35,133),(36,134),(37,135),(38,136),(39,129),(40,130),(41,84),(42,85),(43,86),(44,87),(45,88),(46,81),(47,82),(48,83),(57,100),(58,101),(59,102),(60,103),(61,104),(62,97),(63,98),(64,99),(65,137),(66,138),(67,139),(68,140),(69,141),(70,142),(71,143),(72,144),(105,122),(106,123),(107,124),(108,125),(109,126),(110,127),(111,128),(112,121)], [(1,125,75),(2,76,126),(3,127,77),(4,78,128),(5,121,79),(6,80,122),(7,123,73),(8,74,124),(9,105,51),(10,52,106),(11,107,53),(12,54,108),(13,109,55),(14,56,110),(15,111,49),(16,50,112),(17,36,141),(18,142,37),(19,38,143),(20,144,39),(21,40,137),(22,138,33),(23,34,139),(24,140,35),(25,57,41),(26,42,58),(27,59,43),(28,44,60),(29,61,45),(30,46,62),(31,63,47),(32,48,64),(65,92,130),(66,131,93),(67,94,132),(68,133,95),(69,96,134),(70,135,89),(71,90,136),(72,129,91),(81,97,119),(82,120,98),(83,99,113),(84,114,100),(85,101,115),(86,116,102),(87,103,117),(88,118,104)], [(1,68,82),(2,83,69),(3,70,84),(4,85,71),(5,72,86),(6,87,65),(7,66,88),(8,81,67),(9,60,21),(10,22,61),(11,62,23),(12,24,63),(13,64,17),(14,18,57),(15,58,19),(16,20,59),(25,110,37),(26,38,111),(27,112,39),(28,40,105),(29,106,33),(30,34,107),(31,108,35),(32,36,109),(41,56,142),(42,143,49),(43,50,144),(44,137,51),(45,52,138),(46,139,53),(47,54,140),(48,141,55),(73,93,104),(74,97,94),(75,95,98),(76,99,96),(77,89,100),(78,101,90),(79,91,102),(80,103,92),(113,134,126),(114,127,135),(115,136,128),(116,121,129),(117,130,122),(118,123,131),(119,132,124),(120,125,133)], [(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)]])
72 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | ··· | 3E | 3F | 3G | 3H | 3I | 4A | 4B | 4C | 4D | 6A | ··· | 6E | 6F | 6G | 6H | 6I | 6J | ··· | 6Q | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 12A | ··· | 12J | 12K | ··· | 12R | 12S | ··· | 12Z | 24A | 24B | 24C | 24D |
| order | 1 | 2 | 2 | 2 | 3 | ··· | 3 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 6 | 6 | 6 | 6 | 6 | ··· | 6 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 12 | ··· | 12 | 12 | ··· | 12 | 12 | ··· | 12 | 24 | 24 | 24 | 24 |
| size | 1 | 1 | 3 | 3 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 1 | 1 | 3 | 3 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 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 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | - | + | - | |||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C8 | S3 | S3 | Dic3 | D6 | Dic3 | C3⋊C8 | C4×S3 | S3×C8 | S32 | S3×Dic3 | S3×C3⋊C8 |
| kernel | S3×C32⋊4C8 | C3×C32⋊4C8 | C33⋊7C8 | S3×C3×C12 | C32×Dic3 | S3×C3×C6 | S3×C32 | C32⋊4C8 | S3×C12 | C3×Dic3 | C3×C12 | S3×C6 | C3×S3 | C3×C6 | C32 | C12 | C6 | C3 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 8 | 1 | 4 | 4 | 5 | 4 | 16 | 2 | 4 | 4 | 4 | 8 |
Matrix representation of S3×C32⋊4C8 ►in GL6(𝔽73)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 | 1 |
| 0 | 0 | 0 | 0 | 72 | 0 |
| 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 72 | 1 | 0 | 0 | 0 | 0 |
| 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 1 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 72 | 1 | 0 | 0 | 0 | 0 |
| 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 44 | 54 | 0 | 0 | 0 | 0 |
| 25 | 29 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 51 | 0 | 0 |
| 0 | 0 | 51 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(73))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,1,0],[72,0,0,0,0,0,0,72,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[72,72,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,72,72,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[72,72,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[44,25,0,0,0,0,54,29,0,0,0,0,0,0,0,51,0,0,0,0,51,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
S3×C32⋊4C8 in GAP, Magma, Sage, TeX
S_3\times C_3^2\rtimes_4C_8
% in TeX
G:=Group("S3xC3^2:4C8"); // GroupNames label
G:=SmallGroup(432,430);
// by ID
G=gap.SmallGroup(432,430);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,36,58,571,2028,14118]);
// Polycyclic
G:=Group<a,b,c,d,e|a^3=b^2=c^3=d^3=e^8=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e^-1=c^-1,e*d*e^-1=d^-1>;
// generators/relations