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G = D29  order 58 = 2·29

Dihedral group

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

Aliases: D29, C29⋊C2, sometimes denoted D58 or Dih29 or Dih58, SmallGroup(58,1)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C29 — D29
Chief series
C1 — C29 — D29
Lower central
C29 — D29
Upper central
C1

Generators and relations for D29
 G = < a,b | a29=b2=1, bab=a-1 >

C1
29C2
C29
D29

Character table of D29

 class 1229A29B29C29D29E29F29G29H29I29J29K29L29M29N
 size 12922222222222222
ρ11111111111111111    trivial
ρ21-111111111111111    linear of order 2
ρ320ζ2920+ζ299ζ2928+ζ29ζ2918+ζ2911ζ2921+ζ298ζ2927+ζ292ζ2917+ζ2912ζ2922+ζ297ζ2926+ζ293ζ2916+ζ2913ζ2923+ζ296ζ2925+ζ294ζ2915+ζ2914ζ2924+ζ295ζ2919+ζ2910    orthogonal faithful
ρ420ζ2925+ζ294ζ2923+ζ296ζ2921+ζ298ζ2919+ζ2910ζ2917+ζ2912ζ2915+ζ2914ζ2916+ζ2913ζ2918+ζ2911ζ2920+ζ299ζ2922+ζ297ζ2924+ζ295ζ2926+ζ293ζ2928+ζ29ζ2927+ζ292    orthogonal faithful
ρ520ζ2926+ζ293ζ2919+ζ2910ζ2923+ζ296ζ2922+ζ297ζ2920+ζ299ζ2925+ζ294ζ2917+ζ2912ζ2928+ζ29ζ2915+ζ2914ζ2927+ζ292ζ2918+ζ2911ζ2924+ζ295ζ2921+ζ298ζ2916+ζ2913    orthogonal faithful
ρ620ζ2928+ζ29ζ2916+ζ2913ζ2927+ζ292ζ2917+ζ2912ζ2926+ζ293ζ2918+ζ2911ζ2925+ζ294ζ2919+ζ2910ζ2924+ζ295ζ2920+ζ299ζ2923+ζ296ζ2921+ζ298ζ2922+ζ297ζ2915+ζ2914    orthogonal faithful
ρ720ζ2916+ζ2913ζ2924+ζ295ζ2926+ζ293ζ2918+ζ2911ζ2919+ζ2910ζ2927+ζ292ζ2923+ζ296ζ2915+ζ2914ζ2922+ζ297ζ2928+ζ29ζ2920+ζ299ζ2917+ζ2912ζ2925+ζ294ζ2921+ζ298    orthogonal faithful
ρ820ζ2922+ζ297ζ2925+ζ294ζ2915+ζ2914ζ2926+ζ293ζ2921+ζ298ζ2919+ζ2910ζ2928+ζ29ζ2917+ζ2912ζ2923+ζ296ζ2924+ζ295ζ2916+ζ2913ζ2927+ζ292ζ2920+ζ299ζ2918+ζ2911    orthogonal faithful
ρ920ζ2917+ζ2912ζ2918+ζ2911ζ2924+ζ295ζ2928+ζ29ζ2922+ζ297ζ2916+ζ2913ζ2919+ζ2910ζ2925+ζ294ζ2927+ζ292ζ2921+ζ298ζ2915+ζ2914ζ2920+ζ299ζ2926+ζ293ζ2923+ζ296    orthogonal faithful
ρ1020ζ2923+ζ296ζ2920+ζ299ζ2917+ζ2912ζ2915+ζ2914ζ2918+ζ2911ζ2921+ζ298ζ2924+ζ295ζ2927+ζ292ζ2928+ζ29ζ2925+ζ294ζ2922+ζ297ζ2919+ζ2910ζ2916+ζ2913ζ2926+ζ293    orthogonal faithful
ρ1120ζ2918+ζ2911ζ2927+ζ292ζ2922+ζ297ζ2916+ζ2913ζ2925+ζ294ζ2924+ζ295ζ2915+ζ2914ζ2923+ζ296ζ2926+ζ293ζ2917+ζ2912ζ2921+ζ298ζ2928+ζ29ζ2919+ζ2910ζ2920+ζ299    orthogonal faithful
ρ1220ζ2924+ζ295ζ2922+ζ297ζ2919+ζ2910ζ2927+ζ292ζ2915+ζ2914ζ2926+ζ293ζ2920+ζ299ζ2921+ζ298ζ2925+ζ294ζ2916+ζ2913ζ2928+ζ29ζ2918+ζ2911ζ2923+ζ296ζ2917+ζ2912    orthogonal faithful
ρ1320ζ2921+ζ298ζ2917+ζ2912ζ2916+ζ2913ζ2920+ζ299ζ2924+ζ295ζ2928+ζ29ζ2926+ζ293ζ2922+ζ297ζ2918+ζ2911ζ2915+ζ2914ζ2919+ζ2910ζ2923+ζ296ζ2927+ζ292ζ2925+ζ294    orthogonal faithful
ρ1420ζ2915+ζ2914ζ2921+ζ298ζ2928+ζ29ζ2923+ζ296ζ2916+ζ2913ζ2920+ζ299ζ2927+ζ292ζ2924+ζ295ζ2917+ζ2912ζ2919+ζ2910ζ2926+ζ293ζ2925+ζ294ζ2918+ζ2911ζ2922+ζ297    orthogonal faithful
ρ1520ζ2919+ζ2910ζ2915+ζ2914ζ2920+ζ299ζ2925+ζ294ζ2928+ζ29ζ2923+ζ296ζ2918+ζ2911ζ2916+ζ2913ζ2921+ζ298ζ2926+ζ293ζ2927+ζ292ζ2922+ζ297ζ2917+ζ2912ζ2924+ζ295    orthogonal faithful
ρ1620ζ2927+ζ292ζ2926+ζ293ζ2925+ζ294ζ2924+ζ295ζ2923+ζ296ζ2922+ζ297ζ2921+ζ298ζ2920+ζ299ζ2919+ζ2910ζ2918+ζ2911ζ2917+ζ2912ζ2916+ζ2913ζ2915+ζ2914ζ2928+ζ29    orthogonal faithful

Permutation representations of D29
►On 29 points: primitive - transitive group 29T2
Generators in S29
(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)

(1 29)(2 28)(3 27)(4 26)(5 25)(6 24)(7 23)(8 22)(9 21)(10 20)(11 19)(12 18)(13 17)(14 16)
 
G:=sub<Sym(29)| (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), (1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)>;
 
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), (1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16) );
 
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)], [(1,29),(2,28),(3,27),(4,26),(5,25),(6,24),(7,23),(8,22),(9,21),(10,20),(11,19),(12,18),(13,17),(14,16)]])
 
G:=TransitiveGroup(29,2);
 

D29 is a maximal subgroup of   C29⋊C4  D87  D145  C29⋊C14  D203
D29 is a maximal quotient of   Dic29  D87  D145  D203

Matrix representation of D29 ►in GL2(𝔽59) generated by

1458
10
,
1458
1845
G:=sub<GL(2,GF(59))| [14,1,58,0],[14,18,58,45] >;
 

D29 in GAP, Magma, Sage, TeX 

D_{29}
 
% in TeX
 
G:=Group("D29");
 
// GroupNames label
 
G:=SmallGroup(58,1);
 
// by ID
 
G=gap.SmallGroup(58,1);
 
# by ID
 
G:=PCGroup([2,-2,-29,225]);
 
// Polycyclic
 
G:=Group<a,b|a^29=b^2=1,b*a*b=a^-1>;
 
// generators/relations
 

Export

Subgroup lattice of D29 in TeX
Character table of D29 in TeX

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