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G = D145order 290 = 2·5·29

Dihedral group

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

Aliases: D145, C5⋊D29, C29⋊D5, C1451C2, sometimes denoted D290 or Dih145 or Dih290, SmallGroup(290,3)

Series: Derived Chief Lower central Upper central

C1C145 — D145
C1C29C145 — D145
C145 — D145
C1

Generators and relations for D145
 G = < a,b | a145=b2=1, bab=a-1 >

145C2
29D5
5D29

Smallest permutation representation of D145
On 145 points
Generators in S145
(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)
(1 145)(2 144)(3 143)(4 142)(5 141)(6 140)(7 139)(8 138)(9 137)(10 136)(11 135)(12 134)(13 133)(14 132)(15 131)(16 130)(17 129)(18 128)(19 127)(20 126)(21 125)(22 124)(23 123)(24 122)(25 121)(26 120)(27 119)(28 118)(29 117)(30 116)(31 115)(32 114)(33 113)(34 112)(35 111)(36 110)(37 109)(38 108)(39 107)(40 106)(41 105)(42 104)(43 103)(44 102)(45 101)(46 100)(47 99)(48 98)(49 97)(50 96)(51 95)(52 94)(53 93)(54 92)(55 91)(56 90)(57 89)(58 88)(59 87)(60 86)(61 85)(62 84)(63 83)(64 82)(65 81)(66 80)(67 79)(68 78)(69 77)(70 76)(71 75)(72 74)

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

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

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

74 conjugacy classes

class 1  2 5A5B29A···29N145A···145BD
order125529···29145···145
size1145222···22···2

74 irreducible representations

dim11222
type+++++
imageC1C2D5D29D145
kernelD145C145C29C5C1
# reps1121456

Matrix representation of D145 in GL2(𝔽1451) generated by

22903
548662
,
22903
12481429
G:=sub<GL(2,GF(1451))| [22,548,903,662],[22,1248,903,1429] >;

D145 in GAP, Magma, Sage, TeX

D_{145}
% in TeX

G:=Group("D145");
// GroupNames label

G:=SmallGroup(290,3);
// by ID

G=gap.SmallGroup(290,3);
# by ID

G:=PCGroup([3,-2,-5,-29,49,2522]);
// Polycyclic

G:=Group<a,b|a^145=b^2=1,b*a*b=a^-1>;
// generators/relations

Export

Subgroup lattice of D145 in TeX

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