C₃×C₅×C₃₁₁⋊C₅ #37552257

order	23325
automorphism	?
homology	Abelianization (H₁) = C₃×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product	C₃×C₅×C₃₁₁⋊C₅
unambiguous semidirect product	C₃₁₁⋊(C₃×C₅²)
unambiguous semidirect product	(C₃×C₃₁₁)⋊C₅²
unambiguous semidirect product	(C₅×C₃₁₁)⋊(C₃×C₅)
unambiguous semidirect product	(C₃×C₅×C₃₁₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₃×C₅	C₃₁₁⋊C₅
commutator, cosocle, hypocenter	C₃₁₁	C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₃₁₁	C₅
LCS	G ▷ C₃₁₁
UCS	C₁ ◁ C₃×C₅

32 conjugacy classes of subgroups.

μ_t(G) = 4665

1005 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23325, 4);