A₄×C₂₅₅₁ #44499494

order	30612
automorphism	?
homology	Abelianization (H₁) = C₃×C₂₅₅₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	A₄×C₂₅₅₁
unambiguous semidirect product	C₂²⋊(C₃×C₂₅₅₁)

Fitting, socle, Hall	C₂²×C₂₅₅₁ ⋊ C₃
derived, Sylow	C₂² ⋊ C₃×C₂₅₅₁

	subgroup	G/H
center, hypercenter	C₂₅₅₁	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₂₅₅₁
Frattini	C₁	G
Fitting, socle	C₂²×C₂₅₅₁	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂₅₅₁

10 conjugacy classes of subgroups.

μ_t(G) = 10204

10204 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30612, 10);