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G = C1order 1

Trivial group

trivial, cyclic, perfect

Aliases: C1, also denoted Z1, SmallGroup(1,1)

Series: Derived Chief Lower central Upper central

C1
C1
C1
C1


Character table of C1

 class 1
 size 1
ρ11    trivial faithful

Permutation representations of C1
Regular action on 1 point - transitive group 1T1
Generators in S1

G:=sub<Sym(1)| >;

G:=Group( () );

G=PermutationGroup()

G:=TransitiveGroup(1,1);

Matrix representation of C1 in GL1(ℤ) generated by

G:=sub<GL(1,Integers())|  >;

C1 in GAP, Magma, Sage, TeX

C_1
% in TeX

G:=Group("C1");
// GroupNames label

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

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

G:=PCGroup([IntegerRing()|]);
// Polycyclic

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