Copied to
clipboard

G = D29order 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

C1C29 — D29
C1C29 — D29
C29 — D29
C1

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

29C2

Character table of D29

 class 1229A29B29C29D29E29F29G29H29I29J29K29L29M29N
 size 12922222222222222
ρ11111111111111111    trivial
ρ21-111111111111111    linear of order 2
ρ320ζ2920299ζ292829ζ29182911ζ2921298ζ2927292ζ29172912ζ2922297ζ2926293ζ29162913ζ2923296ζ2925294ζ29152914ζ2924295ζ29192910    orthogonal faithful
ρ420ζ2925294ζ2923296ζ2921298ζ29192910ζ29172912ζ29152914ζ29162913ζ29182911ζ2920299ζ2922297ζ2924295ζ2926293ζ292829ζ2927292    orthogonal faithful
ρ520ζ2926293ζ29192910ζ2923296ζ2922297ζ2920299ζ2925294ζ29172912ζ292829ζ29152914ζ2927292ζ29182911ζ2924295ζ2921298ζ29162913    orthogonal faithful
ρ620ζ292829ζ29162913ζ2927292ζ29172912ζ2926293ζ29182911ζ2925294ζ29192910ζ2924295ζ2920299ζ2923296ζ2921298ζ2922297ζ29152914    orthogonal faithful
ρ720ζ29162913ζ2924295ζ2926293ζ29182911ζ29192910ζ2927292ζ2923296ζ29152914ζ2922297ζ292829ζ2920299ζ29172912ζ2925294ζ2921298    orthogonal faithful
ρ820ζ2922297ζ2925294ζ29152914ζ2926293ζ2921298ζ29192910ζ292829ζ29172912ζ2923296ζ2924295ζ29162913ζ2927292ζ2920299ζ29182911    orthogonal faithful
ρ920ζ29172912ζ29182911ζ2924295ζ292829ζ2922297ζ29162913ζ29192910ζ2925294ζ2927292ζ2921298ζ29152914ζ2920299ζ2926293ζ2923296    orthogonal faithful
ρ1020ζ2923296ζ2920299ζ29172912ζ29152914ζ29182911ζ2921298ζ2924295ζ2927292ζ292829ζ2925294ζ2922297ζ29192910ζ29162913ζ2926293    orthogonal faithful
ρ1120ζ29182911ζ2927292ζ2922297ζ29162913ζ2925294ζ2924295ζ29152914ζ2923296ζ2926293ζ29172912ζ2921298ζ292829ζ29192910ζ2920299    orthogonal faithful
ρ1220ζ2924295ζ2922297ζ29192910ζ2927292ζ29152914ζ2926293ζ2920299ζ2921298ζ2925294ζ29162913ζ292829ζ29182911ζ2923296ζ29172912    orthogonal faithful
ρ1320ζ2921298ζ29172912ζ29162913ζ2920299ζ2924295ζ292829ζ2926293ζ2922297ζ29182911ζ29152914ζ29192910ζ2923296ζ2927292ζ2925294    orthogonal faithful
ρ1420ζ29152914ζ2921298ζ292829ζ2923296ζ29162913ζ2920299ζ2927292ζ2924295ζ29172912ζ29192910ζ2926293ζ2925294ζ29182911ζ2922297    orthogonal faithful
ρ1520ζ29192910ζ29152914ζ2920299ζ2925294ζ292829ζ2923296ζ29182911ζ29162913ζ2921298ζ2926293ζ2927292ζ2922297ζ29172912ζ2924295    orthogonal faithful
ρ1620ζ2927292ζ2926293ζ2925294ζ2924295ζ2923296ζ2922297ζ2921298ζ2920299ζ29192910ζ29182911ζ29172912ζ29162913ζ29152914ζ292829    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);

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

׿
×
𝔽