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G = C23order 23

Cyclic group

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

Aliases: C23, also denoted Z23, SmallGroup(23,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C23
C1 — C23
C1 — C23
C1 — C23
C1 — C23

Generators and relations for C23
 G = < a | a23=1 >


Character table of C23

 class 123A23B23C23D23E23F23G23H23I23J23K23L23M23N23O23P23Q23R23S23T23U23V
 size 11111111111111111111111
ρ111111111111111111111111    trivial
ρ21ζ2322ζ232ζ233ζ234ζ235ζ236ζ237ζ238ζ239ζ2310ζ2311ζ2312ζ2313ζ2314ζ2315ζ2316ζ2317ζ2318ζ2319ζ2320ζ2321ζ23    linear of order 23 faithful
ρ31ζ2321ζ234ζ236ζ238ζ2310ζ2312ζ2314ζ2316ζ2318ζ2320ζ2322ζ23ζ233ζ235ζ237ζ239ζ2311ζ2313ζ2315ζ2317ζ2319ζ232    linear of order 23 faithful
ρ41ζ2320ζ236ζ239ζ2312ζ2315ζ2318ζ2321ζ23ζ234ζ237ζ2310ζ2313ζ2316ζ2319ζ2322ζ232ζ235ζ238ζ2311ζ2314ζ2317ζ233    linear of order 23 faithful
ρ51ζ2319ζ238ζ2312ζ2316ζ2320ζ23ζ235ζ239ζ2313ζ2317ζ2321ζ232ζ236ζ2310ζ2314ζ2318ζ2322ζ233ζ237ζ2311ζ2315ζ234    linear of order 23 faithful
ρ61ζ2318ζ2310ζ2315ζ2320ζ232ζ237ζ2312ζ2317ζ2322ζ234ζ239ζ2314ζ2319ζ23ζ236ζ2311ζ2316ζ2321ζ233ζ238ζ2313ζ235    linear of order 23 faithful
ρ71ζ2317ζ2312ζ2318ζ23ζ237ζ2313ζ2319ζ232ζ238ζ2314ζ2320ζ233ζ239ζ2315ζ2321ζ234ζ2310ζ2316ζ2322ζ235ζ2311ζ236    linear of order 23 faithful
ρ81ζ2316ζ2314ζ2321ζ235ζ2312ζ2319ζ233ζ2310ζ2317ζ23ζ238ζ2315ζ2322ζ236ζ2313ζ2320ζ234ζ2311ζ2318ζ232ζ239ζ237    linear of order 23 faithful
ρ91ζ2315ζ2316ζ23ζ239ζ2317ζ232ζ2310ζ2318ζ233ζ2311ζ2319ζ234ζ2312ζ2320ζ235ζ2313ζ2321ζ236ζ2314ζ2322ζ237ζ238    linear of order 23 faithful
ρ101ζ2314ζ2318ζ234ζ2313ζ2322ζ238ζ2317ζ233ζ2312ζ2321ζ237ζ2316ζ232ζ2311ζ2320ζ236ζ2315ζ23ζ2310ζ2319ζ235ζ239    linear of order 23 faithful
ρ111ζ2313ζ2320ζ237ζ2317ζ234ζ2314ζ23ζ2311ζ2321ζ238ζ2318ζ235ζ2315ζ232ζ2312ζ2322ζ239ζ2319ζ236ζ2316ζ233ζ2310    linear of order 23 faithful
ρ121ζ2312ζ2322ζ2310ζ2321ζ239ζ2320ζ238ζ2319ζ237ζ2318ζ236ζ2317ζ235ζ2316ζ234ζ2315ζ233ζ2314ζ232ζ2313ζ23ζ2311    linear of order 23 faithful
ρ131ζ2311ζ23ζ2313ζ232ζ2314ζ233ζ2315ζ234ζ2316ζ235ζ2317ζ236ζ2318ζ237ζ2319ζ238ζ2320ζ239ζ2321ζ2310ζ2322ζ2312    linear of order 23 faithful
ρ141ζ2310ζ233ζ2316ζ236ζ2319ζ239ζ2322ζ2312ζ232ζ2315ζ235ζ2318ζ238ζ2321ζ2311ζ23ζ2314ζ234ζ2317ζ237ζ2320ζ2313    linear of order 23 faithful
ρ151ζ239ζ235ζ2319ζ2310ζ23ζ2315ζ236ζ2320ζ2311ζ232ζ2316ζ237ζ2321ζ2312ζ233ζ2317ζ238ζ2322ζ2313ζ234ζ2318ζ2314    linear of order 23 faithful
ρ161ζ238ζ237ζ2322ζ2314ζ236ζ2321ζ2313ζ235ζ2320ζ2312ζ234ζ2319ζ2311ζ233ζ2318ζ2310ζ232ζ2317ζ239ζ23ζ2316ζ2315    linear of order 23 faithful
ρ171ζ237ζ239ζ232ζ2318ζ2311ζ234ζ2320ζ2313ζ236ζ2322ζ2315ζ238ζ23ζ2317ζ2310ζ233ζ2319ζ2312ζ235ζ2321ζ2314ζ2316    linear of order 23 faithful
ρ181ζ236ζ2311ζ235ζ2322ζ2316ζ2310ζ234ζ2321ζ2315ζ239ζ233ζ2320ζ2314ζ238ζ232ζ2319ζ2313ζ237ζ23ζ2318ζ2312ζ2317    linear of order 23 faithful
ρ191ζ235ζ2313ζ238ζ233ζ2321ζ2316ζ2311ζ236ζ23ζ2319ζ2314ζ239ζ234ζ2322ζ2317ζ2312ζ237ζ232ζ2320ζ2315ζ2310ζ2318    linear of order 23 faithful
ρ201ζ234ζ2315ζ2311ζ237ζ233ζ2322ζ2318ζ2314ζ2310ζ236ζ232ζ2321ζ2317ζ2313ζ239ζ235ζ23ζ2320ζ2316ζ2312ζ238ζ2319    linear of order 23 faithful
ρ211ζ233ζ2317ζ2314ζ2311ζ238ζ235ζ232ζ2322ζ2319ζ2316ζ2313ζ2310ζ237ζ234ζ23ζ2321ζ2318ζ2315ζ2312ζ239ζ236ζ2320    linear of order 23 faithful
ρ221ζ232ζ2319ζ2317ζ2315ζ2313ζ2311ζ239ζ237ζ235ζ233ζ23ζ2322ζ2320ζ2318ζ2316ζ2314ζ2312ζ2310ζ238ζ236ζ234ζ2321    linear of order 23 faithful
ρ231ζ23ζ2321ζ2320ζ2319ζ2318ζ2317ζ2316ζ2315ζ2314ζ2313ζ2312ζ2311ζ2310ζ239ζ238ζ237ζ236ζ235ζ234ζ233ζ232ζ2322    linear of order 23 faithful

Permutation representations of C23
Regular action on 23 points - transitive group 23T1
Generators in S23
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)

G:=sub<Sym(23)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)>;

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) );

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)])

G:=TransitiveGroup(23,1);

Matrix representation of C23 in GL1(𝔽47) generated by

24
G:=sub<GL(1,GF(47))| [24] >;

C23 in GAP, Magma, Sage, TeX

C_{23}
% in TeX

G:=Group("C23");
// GroupNames label

G:=SmallGroup(23,1);
// by ID

G=gap.SmallGroup(23,1);
# by ID

G:=PCGroup([1,-23]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^23=1>;
// generators/relations

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