C₅²⋊C₃×C₃₃₁ #37613944

order	24825
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₃₁ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²⋊C₃×C₃₃₁
unambiguous semidirect product	C₅²⋊(C₃×C₃₃₁)

Fitting, socle, Hall	C₅²×C₃₃₁ ⋊ C₃
derived, Sylow	C₅² ⋊ C₃×C₃₃₁

	subgroup	G/H
center, hypercenter	C₃₃₁	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₃×C₃₃₁
Frattini	C₁	G
Fitting, socle	C₅²×C₃₃₁	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃₃₁

12 conjugacy classes of subgroups.

μ_t(G) = 4965

3641 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24825, 8);