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G = C₁  order 1

Trivial group

trivial, cyclic, perfect

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

Series: Derived ►Chief ►Lower central ►Upper central

Character table of C₁

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

G:=Group( () );

G=PermutationGroup([])

G:=TransitiveGroup(1,1);

C₁ is a maximal subgroup of
 C_p: C₂  C₃  C₅  C₇  C₁₁  C₁₃  C₁₇  C₁₉ ...
C₁ is a maximal quotient of
 A₅  GL₃(𝔽₂)  A₆
 C_p: C₂  C₃  C₅  C₇  C₁₁  C₁₃  C₁₇  C₁₉ ...

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

Export

Subgroup lattice of C₁ in TeX
Character table of C₁ in TeX