C₅×C₃₁×C₄₁⋊C₅ #44540990

order	31775
automorphism	?
homology	Abelianization (H₁) = C₅²×C₃₁ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅×C₃₁×C₄₁⋊C₅
unambiguous semidirect product	C₄₁⋊(C₅²×C₃₁)
unambiguous semidirect product	(C₅×C₄₁)⋊(C₅×C₃₁)

	subgroup	G/H
center, hypercenter	C₅×C₃₁	C₄₁⋊C₅
commutator, cosocle, hypocenter	C₄₁	C₅²×C₃₁
Frattini	C₁	G
Fitting, socle	C₅×C₃₁×C₄₁	C₅
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₅×C₃₁

32 conjugacy classes of subgroups.

μ_t(G) = 6355

2015 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31775, 10);