C₅×C₂₂₅₁⋊C₃ #46798284

order	33765
automorphism	?
homology	Abelianization (H₁) = C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₂₂₅₁⋊C₃
unambiguous semidirect product	(C₅×C₂₂₅₁)⋊C₃

Fitting, socle, Hall	C₅×C₂₂₅₁ ⋊ C₃
derived, Sylow	C₂₂₅₁ ⋊ C₃×C₅

	subgroup	G/H
center, hypercenter	C₅	C₂₂₅₁⋊C₃
commutator, cosocle, hypocenter	C₂₂₅₁	C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₂₂₅₁	C₃
LCS	G ▷ C₂₂₅₁
UCS	C₁ ◁ C₅

8 conjugacy classes of subgroups.

μ_t(G) = 11255

3765 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33765, 3);