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G = C13order 13

Cyclic group

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

Aliases: C13, also denoted Z13, SmallGroup(13,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C13
C1 — C13
C1 — C13
C1 — C13
C1 — C13

Generators and relations for C13
 G = < a | a13=1 >


Character table of C13

 class 113A13B13C13D13E13F13G13H13I13J13K13L
 size 1111111111111
ρ11111111111111    trivial
ρ21ζ1312ζ132ζ133ζ134ζ135ζ136ζ137ζ138ζ139ζ1310ζ1311ζ13    linear of order 13 faithful
ρ31ζ1311ζ134ζ136ζ138ζ1310ζ1312ζ13ζ133ζ135ζ137ζ139ζ132    linear of order 13 faithful
ρ41ζ1310ζ136ζ139ζ1312ζ132ζ135ζ138ζ1311ζ13ζ134ζ137ζ133    linear of order 13 faithful
ρ51ζ139ζ138ζ1312ζ133ζ137ζ1311ζ132ζ136ζ1310ζ13ζ135ζ134    linear of order 13 faithful
ρ61ζ138ζ1310ζ132ζ137ζ1312ζ134ζ139ζ13ζ136ζ1311ζ133ζ135    linear of order 13 faithful
ρ71ζ137ζ1312ζ135ζ1311ζ134ζ1310ζ133ζ139ζ132ζ138ζ13ζ136    linear of order 13 faithful
ρ81ζ136ζ13ζ138ζ132ζ139ζ133ζ1310ζ134ζ1311ζ135ζ1312ζ137    linear of order 13 faithful
ρ91ζ135ζ133ζ1311ζ136ζ13ζ139ζ134ζ1312ζ137ζ132ζ1310ζ138    linear of order 13 faithful
ρ101ζ134ζ135ζ13ζ1310ζ136ζ132ζ1311ζ137ζ133ζ1312ζ138ζ139    linear of order 13 faithful
ρ111ζ133ζ137ζ134ζ13ζ1311ζ138ζ135ζ132ζ1312ζ139ζ136ζ1310    linear of order 13 faithful
ρ121ζ132ζ139ζ137ζ135ζ133ζ13ζ1312ζ1310ζ138ζ136ζ134ζ1311    linear of order 13 faithful
ρ131ζ13ζ1311ζ1310ζ139ζ138ζ137ζ136ζ135ζ134ζ133ζ132ζ1312    linear of order 13 faithful

Permutation representations of C13
Regular action on 13 points - transitive group 13T1
Generators in S13
(1 2 3 4 5 6 7 8 9 10 11 12 13)

G:=sub<Sym(13)| (1,2,3,4,5,6,7,8,9,10,11,12,13)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13)])

G:=TransitiveGroup(13,1);

Polynomial with Galois group C13 over ℚ
actionf(x)Disc(f)
13T1x13-x12-24x11+19x10+190x9-116x8-601x7+246x6+738x5-215x4-291x3+68x2+10x-1234·5312·832·3172·7192

Matrix representation of C13 in GL1(𝔽53) generated by

13
G:=sub<GL(1,GF(53))| [13] >;

C13 in GAP, Magma, Sage, TeX

C_{13}
% in TeX

G:=Group("C13");
// GroupNames label

G:=SmallGroup(13,1);
// by ID

G=gap.SmallGroup(13,1);
# by ID

G:=PCGroup([1,-13]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^13=1>;
// generators/relations

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