direct product, metabelian, supersoluble, monomial, A-group
Aliases: C2×Dic3×D9, D18.11D6, C62.61D6, C6⋊3(C4×D9), (C6×D9)⋊3C4, C18⋊1(C2×Dic3), (C2×C6).16D18, (C2×C18).16D6, C6.5(S3×Dic3), (Dic3×C18)⋊7C2, C9⋊Dic3⋊5C22, (C22×D9).2S3, C9⋊1(C22×Dic3), C22.12(S3×D9), C6.16(C22×D9), (C6×C18).10C22, (C3×C18).16C23, C18.16(C22×S3), (C3×Dic3).40D6, (C6×Dic3).15S3, (C9×Dic3)⋊6C22, (C6×D9).11C22, C3⋊4(C2×C4×D9), C2.2(C2×S3×D9), C6.35(C2×S32), (C2×C6).22S32, (C2×C6×D9).3C2, (C3×C18)⋊1(C2×C4), (C3×D9)⋊2(C2×C4), (C3×C9)⋊2(C22×C4), C32.3(S3×C2×C4), C3.1(C2×S3×Dic3), (C3×C6).42(C4×S3), (C2×C9⋊Dic3)⋊5C2, (C3×C6).84(C22×S3), SmallGroup(432,304)
Series: Derived ►Chief ►Lower central ►Upper central
| C3×C9 — C2×Dic3×D9 |
Generators and relations for C2×Dic3×D9
G = < a,b,c,d,e | a2=b6=d9=e2=1, c2=b3, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, cd=dc, ce=ec, ede=d-1 >
Subgroups: 860 in 178 conjugacy classes, 69 normal (25 characteristic)
C1, C2, C2, C2, C3, C3, C4, C22, C22, S3, C6, C6, C6, C2×C4, C23, C9, C9, C32, Dic3, Dic3, C12, D6, C2×C6, C2×C6, C22×C4, D9, C18, C18, C18, C3×S3, C3×C6, C3×C6, C4×S3, C2×Dic3, C2×Dic3, C2×C12, C22×S3, C22×C6, C3×C9, Dic9, C36, D18, C2×C18, C2×C18, C3×Dic3, C3⋊Dic3, S3×C6, C62, S3×C2×C4, C22×Dic3, C3×D9, C3×C18, C3×C18, C4×D9, C2×Dic9, C2×C36, C22×D9, S3×Dic3, C6×Dic3, C2×C3⋊Dic3, S3×C2×C6, C9×Dic3, C9⋊Dic3, C6×D9, C6×C18, C2×C4×D9, C2×S3×Dic3, Dic3×D9, Dic3×C18, C2×C9⋊Dic3, C2×C6×D9, C2×Dic3×D9
Quotients: C1, C2, C4, C22, S3, C2×C4, C23, Dic3, D6, C22×C4, D9, C4×S3, C2×Dic3, C22×S3, D18, S32, S3×C2×C4, C22×Dic3, C4×D9, C22×D9, S3×Dic3, C2×S32, S3×D9, C2×C4×D9, C2×S3×Dic3, Dic3×D9, C2×S3×D9, C2×Dic3×D9
►On 144 points
Generators in S144
(1 23)(2 24)(3 25)(4 26)(5 27)(6 19)(7 20)(8 21)(9 22)(10 28)(11 29)(12 30)(13 31)(14 32)(15 33)(16 34)(17 35)(18 36)(37 55)(38 56)(39 57)(40 58)(41 59)(42 60)(43 61)(44 62)(45 63)(46 64)(47 65)(48 66)(49 67)(50 68)(51 69)(52 70)(53 71)(54 72)(73 91)(74 92)(75 93)(76 94)(77 95)(78 96)(79 97)(80 98)(81 99)(82 100)(83 101)(84 102)(85 103)(86 104)(87 105)(88 106)(89 107)(90 108)(109 127)(110 128)(111 129)(112 130)(113 131)(114 132)(115 133)(116 134)(117 135)(118 136)(119 137)(120 138)(121 139)(122 140)(123 141)(124 142)(125 143)(126 144)
(1 17 7 14 4 11)(2 18 8 15 5 12)(3 10 9 16 6 13)(19 31 25 28 22 34)(20 32 26 29 23 35)(21 33 27 30 24 36)(37 52 40 46 43 49)(38 53 41 47 44 50)(39 54 42 48 45 51)(55 70 58 64 61 67)(56 71 59 65 62 68)(57 72 60 66 63 69)(73 88 76 82 79 85)(74 89 77 83 80 86)(75 90 78 84 81 87)(91 106 94 100 97 103)(92 107 95 101 98 104)(93 108 96 102 99 105)(109 121 115 118 112 124)(110 122 116 119 113 125)(111 123 117 120 114 126)(127 139 133 136 130 142)(128 140 134 137 131 143)(129 141 135 138 132 144)
(1 86 14 77)(2 87 15 78)(3 88 16 79)(4 89 17 80)(5 90 18 81)(6 82 10 73)(7 83 11 74)(8 84 12 75)(9 85 13 76)(19 100 28 91)(20 101 29 92)(21 102 30 93)(22 103 31 94)(23 104 32 95)(24 105 33 96)(25 106 34 97)(26 107 35 98)(27 108 36 99)(37 118 46 109)(38 119 47 110)(39 120 48 111)(40 121 49 112)(41 122 50 113)(42 123 51 114)(43 124 52 115)(44 125 53 116)(45 126 54 117)(55 136 64 127)(56 137 65 128)(57 138 66 129)(58 139 67 130)(59 140 68 131)(60 141 69 132)(61 142 70 133)(62 143 71 134)(63 144 72 135)
(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 48)(2 47)(3 46)(4 54)(5 53)(6 52)(7 51)(8 50)(9 49)(10 43)(11 42)(12 41)(13 40)(14 39)(15 38)(16 37)(17 45)(18 44)(19 70)(20 69)(21 68)(22 67)(23 66)(24 65)(25 64)(26 72)(27 71)(28 61)(29 60)(30 59)(31 58)(32 57)(33 56)(34 55)(35 63)(36 62)(73 124)(74 123)(75 122)(76 121)(77 120)(78 119)(79 118)(80 126)(81 125)(82 115)(83 114)(84 113)(85 112)(86 111)(87 110)(88 109)(89 117)(90 116)(91 142)(92 141)(93 140)(94 139)(95 138)(96 137)(97 136)(98 144)(99 143)(100 133)(101 132)(102 131)(103 130)(104 129)(105 128)(106 127)(107 135)(108 134)
G:=sub<Sym(144)| (1,23)(2,24)(3,25)(4,26)(5,27)(6,19)(7,20)(8,21)(9,22)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(37,55)(38,56)(39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(73,91)(74,92)(75,93)(76,94)(77,95)(78,96)(79,97)(80,98)(81,99)(82,100)(83,101)(84,102)(85,103)(86,104)(87,105)(88,106)(89,107)(90,108)(109,127)(110,128)(111,129)(112,130)(113,131)(114,132)(115,133)(116,134)(117,135)(118,136)(119,137)(120,138)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144), (1,17,7,14,4,11)(2,18,8,15,5,12)(3,10,9,16,6,13)(19,31,25,28,22,34)(20,32,26,29,23,35)(21,33,27,30,24,36)(37,52,40,46,43,49)(38,53,41,47,44,50)(39,54,42,48,45,51)(55,70,58,64,61,67)(56,71,59,65,62,68)(57,72,60,66,63,69)(73,88,76,82,79,85)(74,89,77,83,80,86)(75,90,78,84,81,87)(91,106,94,100,97,103)(92,107,95,101,98,104)(93,108,96,102,99,105)(109,121,115,118,112,124)(110,122,116,119,113,125)(111,123,117,120,114,126)(127,139,133,136,130,142)(128,140,134,137,131,143)(129,141,135,138,132,144), (1,86,14,77)(2,87,15,78)(3,88,16,79)(4,89,17,80)(5,90,18,81)(6,82,10,73)(7,83,11,74)(8,84,12,75)(9,85,13,76)(19,100,28,91)(20,101,29,92)(21,102,30,93)(22,103,31,94)(23,104,32,95)(24,105,33,96)(25,106,34,97)(26,107,35,98)(27,108,36,99)(37,118,46,109)(38,119,47,110)(39,120,48,111)(40,121,49,112)(41,122,50,113)(42,123,51,114)(43,124,52,115)(44,125,53,116)(45,126,54,117)(55,136,64,127)(56,137,65,128)(57,138,66,129)(58,139,67,130)(59,140,68,131)(60,141,69,132)(61,142,70,133)(62,143,71,134)(63,144,72,135), (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), (1,48)(2,47)(3,46)(4,54)(5,53)(6,52)(7,51)(8,50)(9,49)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,45)(18,44)(19,70)(20,69)(21,68)(22,67)(23,66)(24,65)(25,64)(26,72)(27,71)(28,61)(29,60)(30,59)(31,58)(32,57)(33,56)(34,55)(35,63)(36,62)(73,124)(74,123)(75,122)(76,121)(77,120)(78,119)(79,118)(80,126)(81,125)(82,115)(83,114)(84,113)(85,112)(86,111)(87,110)(88,109)(89,117)(90,116)(91,142)(92,141)(93,140)(94,139)(95,138)(96,137)(97,136)(98,144)(99,143)(100,133)(101,132)(102,131)(103,130)(104,129)(105,128)(106,127)(107,135)(108,134)>;
G:=Group( (1,23)(2,24)(3,25)(4,26)(5,27)(6,19)(7,20)(8,21)(9,22)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(37,55)(38,56)(39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(73,91)(74,92)(75,93)(76,94)(77,95)(78,96)(79,97)(80,98)(81,99)(82,100)(83,101)(84,102)(85,103)(86,104)(87,105)(88,106)(89,107)(90,108)(109,127)(110,128)(111,129)(112,130)(113,131)(114,132)(115,133)(116,134)(117,135)(118,136)(119,137)(120,138)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144), (1,17,7,14,4,11)(2,18,8,15,5,12)(3,10,9,16,6,13)(19,31,25,28,22,34)(20,32,26,29,23,35)(21,33,27,30,24,36)(37,52,40,46,43,49)(38,53,41,47,44,50)(39,54,42,48,45,51)(55,70,58,64,61,67)(56,71,59,65,62,68)(57,72,60,66,63,69)(73,88,76,82,79,85)(74,89,77,83,80,86)(75,90,78,84,81,87)(91,106,94,100,97,103)(92,107,95,101,98,104)(93,108,96,102,99,105)(109,121,115,118,112,124)(110,122,116,119,113,125)(111,123,117,120,114,126)(127,139,133,136,130,142)(128,140,134,137,131,143)(129,141,135,138,132,144), (1,86,14,77)(2,87,15,78)(3,88,16,79)(4,89,17,80)(5,90,18,81)(6,82,10,73)(7,83,11,74)(8,84,12,75)(9,85,13,76)(19,100,28,91)(20,101,29,92)(21,102,30,93)(22,103,31,94)(23,104,32,95)(24,105,33,96)(25,106,34,97)(26,107,35,98)(27,108,36,99)(37,118,46,109)(38,119,47,110)(39,120,48,111)(40,121,49,112)(41,122,50,113)(42,123,51,114)(43,124,52,115)(44,125,53,116)(45,126,54,117)(55,136,64,127)(56,137,65,128)(57,138,66,129)(58,139,67,130)(59,140,68,131)(60,141,69,132)(61,142,70,133)(62,143,71,134)(63,144,72,135), (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), (1,48)(2,47)(3,46)(4,54)(5,53)(6,52)(7,51)(8,50)(9,49)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,45)(18,44)(19,70)(20,69)(21,68)(22,67)(23,66)(24,65)(25,64)(26,72)(27,71)(28,61)(29,60)(30,59)(31,58)(32,57)(33,56)(34,55)(35,63)(36,62)(73,124)(74,123)(75,122)(76,121)(77,120)(78,119)(79,118)(80,126)(81,125)(82,115)(83,114)(84,113)(85,112)(86,111)(87,110)(88,109)(89,117)(90,116)(91,142)(92,141)(93,140)(94,139)(95,138)(96,137)(97,136)(98,144)(99,143)(100,133)(101,132)(102,131)(103,130)(104,129)(105,128)(106,127)(107,135)(108,134) );
G=PermutationGroup([[(1,23),(2,24),(3,25),(4,26),(5,27),(6,19),(7,20),(8,21),(9,22),(10,28),(11,29),(12,30),(13,31),(14,32),(15,33),(16,34),(17,35),(18,36),(37,55),(38,56),(39,57),(40,58),(41,59),(42,60),(43,61),(44,62),(45,63),(46,64),(47,65),(48,66),(49,67),(50,68),(51,69),(52,70),(53,71),(54,72),(73,91),(74,92),(75,93),(76,94),(77,95),(78,96),(79,97),(80,98),(81,99),(82,100),(83,101),(84,102),(85,103),(86,104),(87,105),(88,106),(89,107),(90,108),(109,127),(110,128),(111,129),(112,130),(113,131),(114,132),(115,133),(116,134),(117,135),(118,136),(119,137),(120,138),(121,139),(122,140),(123,141),(124,142),(125,143),(126,144)], [(1,17,7,14,4,11),(2,18,8,15,5,12),(3,10,9,16,6,13),(19,31,25,28,22,34),(20,32,26,29,23,35),(21,33,27,30,24,36),(37,52,40,46,43,49),(38,53,41,47,44,50),(39,54,42,48,45,51),(55,70,58,64,61,67),(56,71,59,65,62,68),(57,72,60,66,63,69),(73,88,76,82,79,85),(74,89,77,83,80,86),(75,90,78,84,81,87),(91,106,94,100,97,103),(92,107,95,101,98,104),(93,108,96,102,99,105),(109,121,115,118,112,124),(110,122,116,119,113,125),(111,123,117,120,114,126),(127,139,133,136,130,142),(128,140,134,137,131,143),(129,141,135,138,132,144)], [(1,86,14,77),(2,87,15,78),(3,88,16,79),(4,89,17,80),(5,90,18,81),(6,82,10,73),(7,83,11,74),(8,84,12,75),(9,85,13,76),(19,100,28,91),(20,101,29,92),(21,102,30,93),(22,103,31,94),(23,104,32,95),(24,105,33,96),(25,106,34,97),(26,107,35,98),(27,108,36,99),(37,118,46,109),(38,119,47,110),(39,120,48,111),(40,121,49,112),(41,122,50,113),(42,123,51,114),(43,124,52,115),(44,125,53,116),(45,126,54,117),(55,136,64,127),(56,137,65,128),(57,138,66,129),(58,139,67,130),(59,140,68,131),(60,141,69,132),(61,142,70,133),(62,143,71,134),(63,144,72,135)], [(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)], [(1,48),(2,47),(3,46),(4,54),(5,53),(6,52),(7,51),(8,50),(9,49),(10,43),(11,42),(12,41),(13,40),(14,39),(15,38),(16,37),(17,45),(18,44),(19,70),(20,69),(21,68),(22,67),(23,66),(24,65),(25,64),(26,72),(27,71),(28,61),(29,60),(30,59),(31,58),(32,57),(33,56),(34,55),(35,63),(36,62),(73,124),(74,123),(75,122),(76,121),(77,120),(78,119),(79,118),(80,126),(81,125),(82,115),(83,114),(84,113),(85,112),(86,111),(87,110),(88,109),(89,117),(90,116),(91,142),(92,141),(93,140),(94,139),(95,138),(96,137),(97,136),(98,144),(99,143),(100,133),(101,132),(102,131),(103,130),(104,129),(105,128),(106,127),(107,135),(108,134)]])
72 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3A | 3B | 3C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 6A | ··· | 6F | 6G | 6H | 6I | 6J | 6K | 6L | 6M | 9A | 9B | 9C | 9D | 9E | 9F | 12A | 12B | 12C | 12D | 18A | ··· | 18I | 18J | ··· | 18R | 36A | ··· | 36L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 9 | 9 | 9 | 9 | 9 | 9 | 12 | 12 | 12 | 12 | 18 | ··· | 18 | 18 | ··· | 18 | 36 | ··· | 36 |
| size | 1 | 1 | 1 | 1 | 9 | 9 | 9 | 9 | 2 | 2 | 4 | 3 | 3 | 3 | 3 | 27 | 27 | 27 | 27 | 2 | ··· | 2 | 4 | 4 | 4 | 18 | 18 | 18 | 18 | 2 | 2 | 2 | 4 | 4 | 4 | 6 | 6 | 6 | 6 | 2 | ··· | 2 | 4 | ··· | 4 | 6 | ··· | 6 |
72 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | + | + | + | + | + | + | - | + | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C4 | S3 | S3 | Dic3 | D6 | D6 | D6 | D6 | D9 | C4×S3 | D18 | D18 | C4×D9 | S32 | S3×Dic3 | C2×S32 | S3×D9 | Dic3×D9 | C2×S3×D9 |
| kernel | C2×Dic3×D9 | Dic3×D9 | Dic3×C18 | C2×C9⋊Dic3 | C2×C6×D9 | C6×D9 | C22×D9 | C6×Dic3 | D18 | D18 | C2×C18 | C3×Dic3 | C62 | C2×Dic3 | C3×C6 | Dic3 | C2×C6 | C6 | C2×C6 | C6 | C6 | C22 | C2 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 1 | 1 | 4 | 2 | 1 | 2 | 1 | 3 | 4 | 6 | 3 | 12 | 1 | 2 | 1 | 3 | 6 | 3 |
Matrix representation of C2×Dic3×D9 ►in GL6(𝔽37)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 36 | 0 | 0 | 0 |
| 0 | 0 | 0 | 36 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 36 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 36 | 0 | 0 |
| 0 | 0 | 1 | 36 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 31 | 0 | 0 | 0 | 0 |
| 31 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 36 | 0 | 0 |
| 0 | 0 | 36 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 36 | 0 |
| 0 | 0 | 0 | 0 | 0 | 36 |
| 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 | 11 | 20 |
| 0 | 0 | 0 | 0 | 17 | 31 |
| 36 | 0 | 0 | 0 | 0 | 0 |
| 0 | 36 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 11 |
| 0 | 0 | 0 | 0 | 17 | 31 |
G:=sub<GL(6,GF(37))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,36,0,0,0,0,0,0,36,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,36,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,36,36,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,31,0,0,0,0,31,0,0,0,0,0,0,0,0,36,0,0,0,0,36,0,0,0,0,0,0,0,36,0,0,0,0,0,0,36],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,11,17,0,0,0,0,20,31],[36,0,0,0,0,0,0,36,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,6,17,0,0,0,0,11,31] >;
C2×Dic3×D9 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_3\times D_9 % in TeX
G:=Group("C2xDic3xD9"); // GroupNames label
G:=SmallGroup(432,304);
// by ID
G=gap.SmallGroup(432,304);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,56,3091,662,4037,7069]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^6=d^9=e^2=1,c^2=b^3,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e=d^-1>;
// generators/relations