C₃²×C₅₄₁⋊C₅ #37566713

order	24345
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×C₅₄₁⋊C₅
unambiguous semidirect product	(C₃²×C₅₄₁)⋊C₅

Fitting, socle, Hall	C₃²×C₅₄₁ ⋊ C₅
derived, Sylow	C₅₄₁ ⋊ C₃²×C₅

	subgroup	G/H
center, hypercenter	C₃²	C₅₄₁⋊C₅
commutator, cosocle, hypocenter	C₅₄₁	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅₄₁	C₅
LCS	G ▷ C₅₄₁
UCS	C₁ ◁ C₃²

24 conjugacy classes of subgroups.

μ_t(G) = 4869

1017 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24345, 9);