C₂×D₃×C₁₉×ΓL(1,𝔽₃₂) #47977682

order	35340
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₃×C₁₉×ΓL(1,𝔽₃₂)
unambiguous semidirect product	C₃⋊(C₂²×C₁₉×ΓL(1,𝔽₃₂))
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₁₉×ΓL(1,𝔽₃₂))
unambiguous semidirect product	(C₂×D₃×C₃₁)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₂×D₃×C₁₉×C₃₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₃×ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃×C₃₁	C₂²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₃₁	C₂×C₅
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ C₂×C₁₉

80 conjugacy classes of subgroups.

μ_t(G) = 3534

1254 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 154);