C₅²⋊C₃×C₃₃₇ #38760160

order	25275
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₃₇ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²⋊C₃×C₃₃₇
unambiguous semidirect product	C₅²⋊(C₃×C₃₃₇)

Fitting, socle, Hall	C₅²×C₃₃₇ ⋊ C₃
derived, Sylow	C₅² ⋊ C₃×C₃₃₇

	subgroup	G/H
center, hypercenter	C₃₃₇	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₃×C₃₃₇
Frattini	C₁	G
Fitting, socle	C₅²×C₃₃₇	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃₃₇

12 conjugacy classes of subgroups.

μ_t(G) = 5055

3707 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25275, 4);