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G = C29order 29

Cyclic group

p-group, cyclic, elementary abelian, simple, monomial

Aliases: C29, also denoted Z29, SmallGroup(29,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C29
C1 — C29
C1 — C29
C1 — C29
C1 — C29

Generators and relations for C29
 G = < a | a29=1 >


Character table of C29

 class 129A29B29C29D29E29F29G29H29I29J29K29L29M29N29O29P29Q29R29S29T29U29V29W29X29Y29Z29AA29AB
 size 11111111111111111111111111111
ρ111111111111111111111111111111    trivial
ρ21ζ2928ζ292ζ293ζ294ζ295ζ296ζ297ζ298ζ299ζ2910ζ2911ζ2912ζ2913ζ2914ζ2915ζ2916ζ2917ζ2918ζ2919ζ2920ζ2921ζ2922ζ2923ζ2924ζ2925ζ2926ζ2927ζ29    linear of order 29 faithful
ρ31ζ2927ζ294ζ296ζ298ζ2910ζ2912ζ2914ζ2916ζ2918ζ2920ζ2922ζ2924ζ2926ζ2928ζ29ζ293ζ295ζ297ζ299ζ2911ζ2913ζ2915ζ2917ζ2919ζ2921ζ2923ζ2925ζ292    linear of order 29 faithful
ρ41ζ2926ζ296ζ299ζ2912ζ2915ζ2918ζ2921ζ2924ζ2927ζ29ζ294ζ297ζ2910ζ2913ζ2916ζ2919ζ2922ζ2925ζ2928ζ292ζ295ζ298ζ2911ζ2914ζ2917ζ2920ζ2923ζ293    linear of order 29 faithful
ρ51ζ2925ζ298ζ2912ζ2916ζ2920ζ2924ζ2928ζ293ζ297ζ2911ζ2915ζ2919ζ2923ζ2927ζ292ζ296ζ2910ζ2914ζ2918ζ2922ζ2926ζ29ζ295ζ299ζ2913ζ2917ζ2921ζ294    linear of order 29 faithful
ρ61ζ2924ζ2910ζ2915ζ2920ζ2925ζ29ζ296ζ2911ζ2916ζ2921ζ2926ζ292ζ297ζ2912ζ2917ζ2922ζ2927ζ293ζ298ζ2913ζ2918ζ2923ζ2928ζ294ζ299ζ2914ζ2919ζ295    linear of order 29 faithful
ρ71ζ2923ζ2912ζ2918ζ2924ζ29ζ297ζ2913ζ2919ζ2925ζ292ζ298ζ2914ζ2920ζ2926ζ293ζ299ζ2915ζ2921ζ2927ζ294ζ2910ζ2916ζ2922ζ2928ζ295ζ2911ζ2917ζ296    linear of order 29 faithful
ρ81ζ2922ζ2914ζ2921ζ2928ζ296ζ2913ζ2920ζ2927ζ295ζ2912ζ2919ζ2926ζ294ζ2911ζ2918ζ2925ζ293ζ2910ζ2917ζ2924ζ292ζ299ζ2916ζ2923ζ29ζ298ζ2915ζ297    linear of order 29 faithful
ρ91ζ2921ζ2916ζ2924ζ293ζ2911ζ2919ζ2927ζ296ζ2914ζ2922ζ29ζ299ζ2917ζ2925ζ294ζ2912ζ2920ζ2928ζ297ζ2915ζ2923ζ292ζ2910ζ2918ζ2926ζ295ζ2913ζ298    linear of order 29 faithful
ρ101ζ2920ζ2918ζ2927ζ297ζ2916ζ2925ζ295ζ2914ζ2923ζ293ζ2912ζ2921ζ29ζ2910ζ2919ζ2928ζ298ζ2917ζ2926ζ296ζ2915ζ2924ζ294ζ2913ζ2922ζ292ζ2911ζ299    linear of order 29 faithful
ρ111ζ2919ζ2920ζ29ζ2911ζ2921ζ292ζ2912ζ2922ζ293ζ2913ζ2923ζ294ζ2914ζ2924ζ295ζ2915ζ2925ζ296ζ2916ζ2926ζ297ζ2917ζ2927ζ298ζ2918ζ2928ζ299ζ2910    linear of order 29 faithful
ρ121ζ2918ζ2922ζ294ζ2915ζ2926ζ298ζ2919ζ29ζ2912ζ2923ζ295ζ2916ζ2927ζ299ζ2920ζ292ζ2913ζ2924ζ296ζ2917ζ2928ζ2910ζ2921ζ293ζ2914ζ2925ζ297ζ2911    linear of order 29 faithful
ρ131ζ2917ζ2924ζ297ζ2919ζ292ζ2914ζ2926ζ299ζ2921ζ294ζ2916ζ2928ζ2911ζ2923ζ296ζ2918ζ29ζ2913ζ2925ζ298ζ2920ζ293ζ2915ζ2927ζ2910ζ2922ζ295ζ2912    linear of order 29 faithful
ρ141ζ2916ζ2926ζ2910ζ2923ζ297ζ2920ζ294ζ2917ζ29ζ2914ζ2927ζ2911ζ2924ζ298ζ2921ζ295ζ2918ζ292ζ2915ζ2928ζ2912ζ2925ζ299ζ2922ζ296ζ2919ζ293ζ2913    linear of order 29 faithful
ρ151ζ2915ζ2928ζ2913ζ2927ζ2912ζ2926ζ2911ζ2925ζ2910ζ2924ζ299ζ2923ζ298ζ2922ζ297ζ2921ζ296ζ2920ζ295ζ2919ζ294ζ2918ζ293ζ2917ζ292ζ2916ζ29ζ2914    linear of order 29 faithful
ρ161ζ2914ζ29ζ2916ζ292ζ2917ζ293ζ2918ζ294ζ2919ζ295ζ2920ζ296ζ2921ζ297ζ2922ζ298ζ2923ζ299ζ2924ζ2910ζ2925ζ2911ζ2926ζ2912ζ2927ζ2913ζ2928ζ2915    linear of order 29 faithful
ρ171ζ2913ζ293ζ2919ζ296ζ2922ζ299ζ2925ζ2912ζ2928ζ2915ζ292ζ2918ζ295ζ2921ζ298ζ2924ζ2911ζ2927ζ2914ζ29ζ2917ζ294ζ2920ζ297ζ2923ζ2910ζ2926ζ2916    linear of order 29 faithful
ρ181ζ2912ζ295ζ2922ζ2910ζ2927ζ2915ζ293ζ2920ζ298ζ2925ζ2913ζ29ζ2918ζ296ζ2923ζ2911ζ2928ζ2916ζ294ζ2921ζ299ζ2926ζ2914ζ292ζ2919ζ297ζ2924ζ2917    linear of order 29 faithful
ρ191ζ2911ζ297ζ2925ζ2914ζ293ζ2921ζ2910ζ2928ζ2917ζ296ζ2924ζ2913ζ292ζ2920ζ299ζ2927ζ2916ζ295ζ2923ζ2912ζ29ζ2919ζ298ζ2926ζ2915ζ294ζ2922ζ2918    linear of order 29 faithful
ρ201ζ2910ζ299ζ2928ζ2918ζ298ζ2927ζ2917ζ297ζ2926ζ2916ζ296ζ2925ζ2915ζ295ζ2924ζ2914ζ294ζ2923ζ2913ζ293ζ2922ζ2912ζ292ζ2921ζ2911ζ29ζ2920ζ2919    linear of order 29 faithful
ρ211ζ299ζ2911ζ292ζ2922ζ2913ζ294ζ2924ζ2915ζ296ζ2926ζ2917ζ298ζ2928ζ2919ζ2910ζ29ζ2921ζ2912ζ293ζ2923ζ2914ζ295ζ2925ζ2916ζ297ζ2927ζ2918ζ2920    linear of order 29 faithful
ρ221ζ298ζ2913ζ295ζ2926ζ2918ζ2910ζ292ζ2923ζ2915ζ297ζ2928ζ2920ζ2912ζ294ζ2925ζ2917ζ299ζ29ζ2922ζ2914ζ296ζ2927ζ2919ζ2911ζ293ζ2924ζ2916ζ2921    linear of order 29 faithful
ρ231ζ297ζ2915ζ298ζ29ζ2923ζ2916ζ299ζ292ζ2924ζ2917ζ2910ζ293ζ2925ζ2918ζ2911ζ294ζ2926ζ2919ζ2912ζ295ζ2927ζ2920ζ2913ζ296ζ2928ζ2921ζ2914ζ2922    linear of order 29 faithful
ρ241ζ296ζ2917ζ2911ζ295ζ2928ζ2922ζ2916ζ2910ζ294ζ2927ζ2921ζ2915ζ299ζ293ζ2926ζ2920ζ2914ζ298ζ292ζ2925ζ2919ζ2913ζ297ζ29ζ2924ζ2918ζ2912ζ2923    linear of order 29 faithful
ρ251ζ295ζ2919ζ2914ζ299ζ294ζ2928ζ2923ζ2918ζ2913ζ298ζ293ζ2927ζ2922ζ2917ζ2912ζ297ζ292ζ2926ζ2921ζ2916ζ2911ζ296ζ29ζ2925ζ2920ζ2915ζ2910ζ2924    linear of order 29 faithful
ρ261ζ294ζ2921ζ2917ζ2913ζ299ζ295ζ29ζ2926ζ2922ζ2918ζ2914ζ2910ζ296ζ292ζ2927ζ2923ζ2919ζ2915ζ2911ζ297ζ293ζ2928ζ2924ζ2920ζ2916ζ2912ζ298ζ2925    linear of order 29 faithful
ρ271ζ293ζ2923ζ2920ζ2917ζ2914ζ2911ζ298ζ295ζ292ζ2928ζ2925ζ2922ζ2919ζ2916ζ2913ζ2910ζ297ζ294ζ29ζ2927ζ2924ζ2921ζ2918ζ2915ζ2912ζ299ζ296ζ2926    linear of order 29 faithful
ρ281ζ292ζ2925ζ2923ζ2921ζ2919ζ2917ζ2915ζ2913ζ2911ζ299ζ297ζ295ζ293ζ29ζ2928ζ2926ζ2924ζ2922ζ2920ζ2918ζ2916ζ2914ζ2912ζ2910ζ298ζ296ζ294ζ2927    linear of order 29 faithful
ρ291ζ29ζ2927ζ2926ζ2925ζ2924ζ2923ζ2922ζ2921ζ2920ζ2919ζ2918ζ2917ζ2916ζ2915ζ2914ζ2913ζ2912ζ2911ζ2910ζ299ζ298ζ297ζ296ζ295ζ294ζ293ζ292ζ2928    linear of order 29 faithful

Permutation representations of C29
Regular action on 29 points - transitive group 29T1
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)

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)>;

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) );

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)])

G:=TransitiveGroup(29,1);

Matrix representation of C29 in GL1(𝔽59) generated by

9
G:=sub<GL(1,GF(59))| [9] >;

C29 in GAP, Magma, Sage, TeX

C_{29}
% in TeX

G:=Group("C29");
// GroupNames label

G:=SmallGroup(29,1);
// by ID

G=gap.SmallGroup(29,1);
# by ID

G:=PCGroup([1,-29]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^29=1>;
// generators/relations

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