C₅²⋊C₃×C₃₁₁ #37552258

order	23325
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₁₁ · Schur multiplier (H₂) = C₅

Aliases

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

Fitting, socle, Hall	C₅²×C₃₁₁ ⋊ C₃
derived, Sylow	C₅² ⋊ C₃×C₃₁₁

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

12 conjugacy classes of subgroups.

μ_t(G) = 4665

3421 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23325, 5);