C₅×C₄₃×ΓL(1,𝔽₃₂) #45686708

order	33325
automorphism	?
homology	Abelianization (H₁) = C₅²×C₄₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅×C₄₃×ΓL(1,𝔽₃₂)
unambiguous semidirect product	C₃₁⋊(C₅²×C₄₃)
unambiguous semidirect product	(C₅×C₃₁)⋊(C₅×C₄₃)
unambiguous semidirect product	(C₃₁×C₄₃)⋊C₅²
unambiguous semidirect product	(C₅×C₃₁×C₄₃)⋊C₅

	subgroup	G/H
center, hypercenter	C₅×C₄₃	ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃₁	C₅²×C₄₃
Frattini	C₁	G
Fitting, socle	C₅×C₃₁×C₄₃	C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₅×C₄₃

32 conjugacy classes of subgroups.

μ_t(G) = 6665

2365 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33325, 4);