metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: D141, C47⋊S3, C3⋊D47, C141⋊1C2, sometimes denoted D282 or Dih141 or Dih282, SmallGroup(282,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C141 — D141 |
Generators and relations for D141
G = < a,b | a141=b2=1, bab=a-1 >
Smallest permutation representation of D141
►On 141 points
Generators in S141
(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)
(1 141)(2 140)(3 139)(4 138)(5 137)(6 136)(7 135)(8 134)(9 133)(10 132)(11 131)(12 130)(13 129)(14 128)(15 127)(16 126)(17 125)(18 124)(19 123)(20 122)(21 121)(22 120)(23 119)(24 118)(25 117)(26 116)(27 115)(28 114)(29 113)(30 112)(31 111)(32 110)(33 109)(34 108)(35 107)(36 106)(37 105)(38 104)(39 103)(40 102)(41 101)(42 100)(43 99)(44 98)(45 97)(46 96)(47 95)(48 94)(49 93)(50 92)(51 91)(52 90)(53 89)(54 88)(55 87)(56 86)(57 85)(58 84)(59 83)(60 82)(61 81)(62 80)(63 79)(64 78)(65 77)(66 76)(67 75)(68 74)(69 73)(70 72)
G:=sub<Sym(141)| (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), (1,141)(2,140)(3,139)(4,138)(5,137)(6,136)(7,135)(8,134)(9,133)(10,132)(11,131)(12,130)(13,129)(14,128)(15,127)(16,126)(17,125)(18,124)(19,123)(20,122)(21,121)(22,120)(23,119)(24,118)(25,117)(26,116)(27,115)(28,114)(29,113)(30,112)(31,111)(32,110)(33,109)(34,108)(35,107)(36,106)(37,105)(38,104)(39,103)(40,102)(41,101)(42,100)(43,99)(44,98)(45,97)(46,96)(47,95)(48,94)(49,93)(50,92)(51,91)(52,90)(53,89)(54,88)(55,87)(56,86)(57,85)(58,84)(59,83)(60,82)(61,81)(62,80)(63,79)(64,78)(65,77)(66,76)(67,75)(68,74)(69,73)(70,72)>;
G:=Group( (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), (1,141)(2,140)(3,139)(4,138)(5,137)(6,136)(7,135)(8,134)(9,133)(10,132)(11,131)(12,130)(13,129)(14,128)(15,127)(16,126)(17,125)(18,124)(19,123)(20,122)(21,121)(22,120)(23,119)(24,118)(25,117)(26,116)(27,115)(28,114)(29,113)(30,112)(31,111)(32,110)(33,109)(34,108)(35,107)(36,106)(37,105)(38,104)(39,103)(40,102)(41,101)(42,100)(43,99)(44,98)(45,97)(46,96)(47,95)(48,94)(49,93)(50,92)(51,91)(52,90)(53,89)(54,88)(55,87)(56,86)(57,85)(58,84)(59,83)(60,82)(61,81)(62,80)(63,79)(64,78)(65,77)(66,76)(67,75)(68,74)(69,73)(70,72) );
G=PermutationGroup([[(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)], [(1,141),(2,140),(3,139),(4,138),(5,137),(6,136),(7,135),(8,134),(9,133),(10,132),(11,131),(12,130),(13,129),(14,128),(15,127),(16,126),(17,125),(18,124),(19,123),(20,122),(21,121),(22,120),(23,119),(24,118),(25,117),(26,116),(27,115),(28,114),(29,113),(30,112),(31,111),(32,110),(33,109),(34,108),(35,107),(36,106),(37,105),(38,104),(39,103),(40,102),(41,101),(42,100),(43,99),(44,98),(45,97),(46,96),(47,95),(48,94),(49,93),(50,92),(51,91),(52,90),(53,89),(54,88),(55,87),(56,86),(57,85),(58,84),(59,83),(60,82),(61,81),(62,80),(63,79),(64,78),(65,77),(66,76),(67,75),(68,74),(69,73),(70,72)]])
72 conjugacy classes
| class | 1 | 2 | 3 | 47A | ··· | 47W | 141A | ··· | 141AT |
| order | 1 | 2 | 3 | 47 | ··· | 47 | 141 | ··· | 141 |
| size | 1 | 141 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
72 irreducible representations
| dim | 1 | 1 | 2 | 2 | 2 |
| type | + | + | + | + | + |
| image | C1 | C2 | S3 | D47 | D141 |
| kernel | D141 | C141 | C47 | C3 | C1 |
| # reps | 1 | 1 | 1 | 23 | 46 |
Matrix representation of D141 ►in GL2(𝔽283) generated by
| 219 | 274 |
| 9 | 72 |
| 219 | 274 |
| 172 | 64 |
G:=sub<GL(2,GF(283))| [219,9,274,72],[219,172,274,64] >;
D141 in GAP, Magma, Sage, TeX
D_{141} % in TeX
G:=Group("D141"); // GroupNames label
G:=SmallGroup(282,3);
// by ID
G=gap.SmallGroup(282,3);
# by ID
G:=PCGroup([3,-2,-3,-47,25,2486]);
// Polycyclic
G:=Group<a,b|a^141=b^2=1,b*a*b=a^-1>;
// generators/relations
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