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G = C25order 25 = 52

Cyclic group

p-group, cyclic, abelian, monomial

Aliases: C25, also denoted Z25, SmallGroup(25,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C25
C1C5 — C25
C1 — C25
C1 — C25
C1C5C5C5C5 — C25

Generators and relations for C25
 G = < a | a25=1 >


Character table of C25

 class 15A5B5C5D25A25B25C25D25E25F25G25H25I25J25K25L25M25N25O25P25Q25R25S25T
 size 1111111111111111111111111
ρ11111111111111111111111111    trivial
ρ21ζ255ζ2510ζ2515ζ2520ζ254ζ2517ζ2513ζ259ζ25ζ256ζ2511ζ2516ζ2522ζ252ζ257ζ2512ζ2518ζ2523ζ253ζ258ζ2514ζ2519ζ2524ζ2521    linear of order 25 faithful
ρ31ζ2510ζ2520ζ255ζ2515ζ258ζ259ζ25ζ2518ζ252ζ2512ζ2522ζ257ζ2519ζ254ζ2514ζ2524ζ2511ζ2521ζ256ζ2516ζ253ζ2513ζ2523ζ2517    linear of order 25 faithful
ρ41ζ2515ζ255ζ2520ζ2510ζ2512ζ25ζ2514ζ252ζ253ζ2518ζ258ζ2523ζ2516ζ256ζ2521ζ2511ζ254ζ2519ζ259ζ2524ζ2517ζ257ζ2522ζ2513    linear of order 25 faithful
ρ51ζ2520ζ2515ζ2510ζ255ζ2516ζ2518ζ252ζ2511ζ254ζ2524ζ2519ζ2514ζ2513ζ258ζ253ζ2523ζ2522ζ2517ζ2512ζ257ζ256ζ25ζ2521ζ259    linear of order 25 faithful
ρ611111ζ54ζ52ζ53ζ54ζ5ζ5ζ5ζ5ζ52ζ52ζ52ζ52ζ53ζ53ζ53ζ53ζ54ζ54ζ54ζ5    linear of order 5
ρ71ζ255ζ2510ζ2515ζ2520ζ2524ζ252ζ253ζ254ζ256ζ2511ζ2516ζ2521ζ257ζ2512ζ2517ζ2522ζ258ζ2513ζ2518ζ2523ζ259ζ2514ζ2519ζ25    linear of order 25 faithful
ρ81ζ2510ζ2520ζ255ζ2515ζ253ζ2519ζ2516ζ2513ζ257ζ2517ζ252ζ2512ζ254ζ2514ζ2524ζ259ζ25ζ2511ζ2521ζ256ζ2523ζ258ζ2518ζ2522    linear of order 25 faithful
ρ91ζ2515ζ255ζ2520ζ2510ζ257ζ2511ζ254ζ2522ζ258ζ2523ζ2513ζ253ζ25ζ2516ζ256ζ2521ζ2519ζ259ζ2524ζ2514ζ2512ζ252ζ2517ζ2518    linear of order 25 faithful
ρ101ζ2520ζ2515ζ2510ζ255ζ2511ζ253ζ2517ζ256ζ259ζ254ζ2524ζ2519ζ2523ζ2518ζ2513ζ258ζ2512ζ257ζ252ζ2522ζ25ζ2521ζ2516ζ2514    linear of order 25 faithful
ρ1111111ζ53ζ54ζ5ζ53ζ52ζ52ζ52ζ52ζ54ζ54ζ54ζ54ζ5ζ5ζ5ζ5ζ53ζ53ζ53ζ52    linear of order 5
ρ121ζ255ζ2510ζ2515ζ2520ζ2519ζ2512ζ2518ζ2524ζ2511ζ2516ζ2521ζ25ζ2517ζ2522ζ252ζ257ζ2523ζ253ζ258ζ2513ζ254ζ259ζ2514ζ256    linear of order 25 faithful
ρ131ζ2510ζ2520ζ255ζ2515ζ2523ζ254ζ256ζ258ζ2512ζ2522ζ257ζ2517ζ2514ζ2524ζ259ζ2519ζ2516ζ25ζ2511ζ2521ζ2518ζ253ζ2513ζ252    linear of order 25 faithful
ρ141ζ2515ζ255ζ2520ζ2510ζ252ζ2521ζ2519ζ2517ζ2513ζ253ζ2518ζ258ζ2511ζ25ζ2516ζ256ζ259ζ2524ζ2514ζ254ζ257ζ2522ζ2512ζ2523    linear of order 25 faithful
ρ151ζ2520ζ2515ζ2510ζ255ζ256ζ2513ζ257ζ25ζ2514ζ259ζ254ζ2524ζ258ζ253ζ2523ζ2518ζ252ζ2522ζ2517ζ2512ζ2521ζ2516ζ2511ζ2519    linear of order 25 faithful
ρ1611111ζ52ζ5ζ54ζ52ζ53ζ53ζ53ζ53ζ5ζ5ζ5ζ5ζ54ζ54ζ54ζ54ζ52ζ52ζ52ζ53    linear of order 5
ρ171ζ255ζ2510ζ2515ζ2520ζ2514ζ2522ζ258ζ2519ζ2516ζ2521ζ25ζ256ζ252ζ257ζ2512ζ2517ζ2513ζ2518ζ2523ζ253ζ2524ζ254ζ259ζ2511    linear of order 25 faithful
ρ181ζ2510ζ2520ζ255ζ2515ζ2518ζ2514ζ2521ζ253ζ2517ζ252ζ2512ζ2522ζ2524ζ259ζ2519ζ254ζ256ζ2516ζ25ζ2511ζ2513ζ2523ζ258ζ257    linear of order 25 faithful
ρ191ζ2515ζ255ζ2520ζ2510ζ2522ζ256ζ259ζ2512ζ2518ζ258ζ2523ζ2513ζ2521ζ2511ζ25ζ2516ζ2524ζ2514ζ254ζ2519ζ252ζ2517ζ257ζ253    linear of order 25 faithful
ρ201ζ2520ζ2515ζ2510ζ255ζ25ζ2523ζ2522ζ2521ζ2519ζ2514ζ259ζ254ζ2518ζ2513ζ258ζ253ζ2517ζ2512ζ257ζ252ζ2516ζ2511ζ256ζ2524    linear of order 25 faithful
ρ2111111ζ5ζ53ζ52ζ5ζ54ζ54ζ54ζ54ζ53ζ53ζ53ζ53ζ52ζ52ζ52ζ52ζ5ζ5ζ5ζ54    linear of order 5
ρ221ζ255ζ2510ζ2515ζ2520ζ259ζ257ζ2523ζ2514ζ2521ζ25ζ256ζ2511ζ2512ζ2517ζ2522ζ252ζ253ζ258ζ2513ζ2518ζ2519ζ2524ζ254ζ2516    linear of order 25 faithful
ρ231ζ2510ζ2520ζ255ζ2515ζ2513ζ2524ζ2511ζ2523ζ2522ζ257ζ2517ζ252ζ259ζ2519ζ254ζ2514ζ2521ζ256ζ2516ζ25ζ258ζ2518ζ253ζ2512    linear of order 25 faithful
ρ241ζ2515ζ255ζ2520ζ2510ζ2517ζ2516ζ2524ζ257ζ2523ζ2513ζ253ζ2518ζ256ζ2521ζ2511ζ25ζ2514ζ254ζ2519ζ259ζ2522ζ2512ζ252ζ258    linear of order 25 faithful
ρ251ζ2520ζ2515ζ2510ζ255ζ2521ζ258ζ2512ζ2516ζ2524ζ2519ζ2514ζ259ζ253ζ2523ζ2518ζ2513ζ257ζ252ζ2522ζ2517ζ2511ζ256ζ25ζ254    linear of order 25 faithful

Permutation representations of C25
Regular action on 25 points - transitive group 25T1
Generators in S25
(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)

G:=sub<Sym(25)| (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)>;

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) );

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)])

G:=TransitiveGroup(25,1);

Matrix representation of C25 in GL1(𝔽101) generated by

80
G:=sub<GL(1,GF(101))| [80] >;

C25 in GAP, Magma, Sage, TeX

C_{25}
% in TeX

G:=Group("C25");
// GroupNames label

G:=SmallGroup(25,1);
// by ID

G=gap.SmallGroup(25,1);
# by ID

G:=PCGroup([2,-5,-5,10]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^25=1>;
// generators/relations

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