Copied to
clipboard

G = D149order 298 = 2·149

Dihedral group

metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: D149, C149⋊C2, sometimes denoted D298 or Dih149 or Dih298, SmallGroup(298,1)

Series: Derived Chief Lower central Upper central

C1C149 — D149
C1C149 — D149
C149 — D149
C1

Generators and relations for D149
 G = < a,b | a149=b2=1, bab=a-1 >

149C2

Smallest permutation representation of D149
On 149 points: primitive
Generators in S149
(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149)
(1 149)(2 148)(3 147)(4 146)(5 145)(6 144)(7 143)(8 142)(9 141)(10 140)(11 139)(12 138)(13 137)(14 136)(15 135)(16 134)(17 133)(18 132)(19 131)(20 130)(21 129)(22 128)(23 127)(24 126)(25 125)(26 124)(27 123)(28 122)(29 121)(30 120)(31 119)(32 118)(33 117)(34 116)(35 115)(36 114)(37 113)(38 112)(39 111)(40 110)(41 109)(42 108)(43 107)(44 106)(45 105)(46 104)(47 103)(48 102)(49 101)(50 100)(51 99)(52 98)(53 97)(54 96)(55 95)(56 94)(57 93)(58 92)(59 91)(60 90)(61 89)(62 88)(63 87)(64 86)(65 85)(66 84)(67 83)(68 82)(69 81)(70 80)(71 79)(72 78)(73 77)(74 76)

G:=sub<Sym(149)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149), (1,149)(2,148)(3,147)(4,146)(5,145)(6,144)(7,143)(8,142)(9,141)(10,140)(11,139)(12,138)(13,137)(14,136)(15,135)(16,134)(17,133)(18,132)(19,131)(20,130)(21,129)(22,128)(23,127)(24,126)(25,125)(26,124)(27,123)(28,122)(29,121)(30,120)(31,119)(32,118)(33,117)(34,116)(35,115)(36,114)(37,113)(38,112)(39,111)(40,110)(41,109)(42,108)(43,107)(44,106)(45,105)(46,104)(47,103)(48,102)(49,101)(50,100)(51,99)(52,98)(53,97)(54,96)(55,95)(56,94)(57,93)(58,92)(59,91)(60,90)(61,89)(62,88)(63,87)(64,86)(65,85)(66,84)(67,83)(68,82)(69,81)(70,80)(71,79)(72,78)(73,77)(74,76)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149), (1,149)(2,148)(3,147)(4,146)(5,145)(6,144)(7,143)(8,142)(9,141)(10,140)(11,139)(12,138)(13,137)(14,136)(15,135)(16,134)(17,133)(18,132)(19,131)(20,130)(21,129)(22,128)(23,127)(24,126)(25,125)(26,124)(27,123)(28,122)(29,121)(30,120)(31,119)(32,118)(33,117)(34,116)(35,115)(36,114)(37,113)(38,112)(39,111)(40,110)(41,109)(42,108)(43,107)(44,106)(45,105)(46,104)(47,103)(48,102)(49,101)(50,100)(51,99)(52,98)(53,97)(54,96)(55,95)(56,94)(57,93)(58,92)(59,91)(60,90)(61,89)(62,88)(63,87)(64,86)(65,85)(66,84)(67,83)(68,82)(69,81)(70,80)(71,79)(72,78)(73,77)(74,76) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149)], [(1,149),(2,148),(3,147),(4,146),(5,145),(6,144),(7,143),(8,142),(9,141),(10,140),(11,139),(12,138),(13,137),(14,136),(15,135),(16,134),(17,133),(18,132),(19,131),(20,130),(21,129),(22,128),(23,127),(24,126),(25,125),(26,124),(27,123),(28,122),(29,121),(30,120),(31,119),(32,118),(33,117),(34,116),(35,115),(36,114),(37,113),(38,112),(39,111),(40,110),(41,109),(42,108),(43,107),(44,106),(45,105),(46,104),(47,103),(48,102),(49,101),(50,100),(51,99),(52,98),(53,97),(54,96),(55,95),(56,94),(57,93),(58,92),(59,91),(60,90),(61,89),(62,88),(63,87),(64,86),(65,85),(66,84),(67,83),(68,82),(69,81),(70,80),(71,79),(72,78),(73,77),(74,76)])

76 conjugacy classes

class 1  2 149A···149BV
order12149···149
size11492···2

76 irreducible representations

dim112
type+++
imageC1C2D149
kernelD149C149C1
# reps1174

Matrix representation of D149 in GL2(𝔽1193) generated by

2781192
10
,
2781192
931915
G:=sub<GL(2,GF(1193))| [278,1,1192,0],[278,931,1192,915] >;

D149 in GAP, Magma, Sage, TeX

D_{149}
% in TeX

G:=Group("D149");
// GroupNames label

G:=SmallGroup(298,1);
// by ID

G=gap.SmallGroup(298,1);
# by ID

G:=PCGroup([2,-2,-149,1185]);
// Polycyclic

G:=Group<a,b|a^149=b^2=1,b*a*b=a^-1>;
// generators/relations

Export

Subgroup lattice of D149 in TeX

׿
×
𝔽