C₃×C₁₅₃₁⋊C₅ #37525833

order	22965
automorphism	?
homology	Abelianization (H₁) = C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₅₃₁⋊C₅
unambiguous semidirect product	(C₃×C₁₅₃₁)⋊C₅

Fitting, socle, Hall	C₃×C₁₅₃₁ ⋊ C₅
derived, Sylow	C₁₅₃₁ ⋊ C₃×C₅

	subgroup	G/H
center, hypercenter	C₃	C₁₅₃₁⋊C₅
commutator, cosocle, hypocenter	C₁₅₃₁	C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₁₅₃₁	C₅
LCS	G ▷ C₁₅₃₁
UCS	C₁ ◁ C₃

8 conjugacy classes of subgroups.

μ_t(G) = 4593

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22965, 2);