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G = C11order 11

Cyclic group

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

Aliases: C11, also denoted Z11, SmallGroup(11,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C11
C1 — C11
C1 — C11
C1 — C11
C1 — C11

Generators and relations for C11
 G = < a | a11=1 >


Character table of C11

 class 111A11B11C11D11E11F11G11H11I11J
 size 11111111111
ρ111111111111    trivial
ρ21ζ1110ζ112ζ113ζ114ζ115ζ116ζ117ζ118ζ119ζ11    linear of order 11 faithful
ρ31ζ119ζ114ζ116ζ118ζ1110ζ11ζ113ζ115ζ117ζ112    linear of order 11 faithful
ρ41ζ118ζ116ζ119ζ11ζ114ζ117ζ1110ζ112ζ115ζ113    linear of order 11 faithful
ρ51ζ117ζ118ζ11ζ115ζ119ζ112ζ116ζ1110ζ113ζ114    linear of order 11 faithful
ρ61ζ116ζ1110ζ114ζ119ζ113ζ118ζ112ζ117ζ11ζ115    linear of order 11 faithful
ρ71ζ115ζ11ζ117ζ112ζ118ζ113ζ119ζ114ζ1110ζ116    linear of order 11 faithful
ρ81ζ114ζ113ζ1110ζ116ζ112ζ119ζ115ζ11ζ118ζ117    linear of order 11 faithful
ρ91ζ113ζ115ζ112ζ1110ζ117ζ114ζ11ζ119ζ116ζ118    linear of order 11 faithful
ρ101ζ112ζ117ζ115ζ113ζ11ζ1110ζ118ζ116ζ114ζ119    linear of order 11 faithful
ρ111ζ11ζ119ζ118ζ117ζ116ζ115ζ114ζ113ζ112ζ1110    linear of order 11 faithful

Permutation representations of C11
Regular action on 11 points - transitive group 11T1
Generators in S11
(1 2 3 4 5 6 7 8 9 10 11)

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

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

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

G:=TransitiveGroup(11,1);

Polynomial with Galois group C11 over ℚ
actionf(x)Disc(f)
11T1x11+x10-10x9-9x8+36x7+28x6-56x5-35x4+35x3+15x2-6x-12310

Matrix representation of C11 in GL1(𝔽23) generated by

8
G:=sub<GL(1,GF(23))| [8] >;

C11 in GAP, Magma, Sage, TeX

C_{11}
% in TeX

G:=Group("C11");
// GroupNames label

G:=SmallGroup(11,1);
// by ID

G=gap.SmallGroup(11,1);
# by ID

G:=PCGroup([1,-11]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^11=1>;
// generators/relations

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