A₄×C₁₇×ΓL(1,𝔽₃₂) #44539299

order	31620
automorphism	?
homology	Abelianization (H₁) = C₃×C₅×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	A₄×C₁₇×ΓL(1,𝔽₃₂)
unambiguous semidirect product	C₂²⋊(C₃×C₁₇×ΓL(1,𝔽₃₂))
unambiguous semidirect product	(C₂²×C₁₇)⋊(C₃×ΓL(1,𝔽₃₂))
unambiguous semidirect product	(A₄×C₃₁)⋊(C₅×C₁₇)
unambiguous semidirect product	(A₄×C₁₇×C₃₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₁₇	A₄×ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₂²×C₃₁	C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₂²×C₁₇×C₃₁	C₃×C₅
LCS	G ▷ C₂²×C₃₁
UCS	C₁ ◁ C₁₇

40 conjugacy classes of subgroups.

μ_t(G) = 2108

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 56);