Finite Group Databasebeta

← Prev (#22576526) Next (#22576528) →

C₄×C₇×C₃₁₁ #22576527

order	8708
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₅×C₃₁ (order 3720) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₅×C₃₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₈₇₀₈
abelian	C₄×C₇×C₃₁₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂	C₂×C₇×C₃₁₁
socle	C₂×C₇×C₃₁₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8708 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₈₇₀₈, D₁₇₄₁₆
Fitting subgroup of	C₄×ΓL(1,𝔽₈)×C₃₁₁
maximal subgroup of	C₃×C₄×C₇×C₃₁₁, C₄×ΓL(1,𝔽₈)×C₃₁₁, C₇×Dic₃×C₃₁₁, …
maximal normal subgroup of	C₃×C₄×C₇×C₃₁₁, C₄×ΓL(1,𝔽₈)×C₃₁₁, C₇×C₈×C₃₁₁, …
maximal quotient of	C₃×C₄×C₇×C₃₁₁, C₇×Dic₃×C₃₁₁, C₇×C₈×C₃₁₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8708, 1);