C₅×C₂₁₆₁⋊C₃ #44569505

order	32415
automorphism	?
homology	Abelianization (H₁) = C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₂₁₆₁⋊C₃
unambiguous semidirect product	(C₅×C₂₁₆₁)⋊C₃

Fitting, socle, Hall	C₅×C₂₁₆₁ ⋊ C₃
derived, Sylow	C₂₁₆₁ ⋊ C₃×C₅

	subgroup	G/H
center, hypercenter	C₅	C₂₁₆₁⋊C₃
commutator, cosocle, hypocenter	C₂₁₆₁	C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₂₁₆₁	C₃
LCS	G ▷ C₂₁₆₁
UCS	C₁ ◁ C₅

8 conjugacy classes of subgroups.

μ_t(G) = 10805

3615 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32415, 3);