C₅²⋊C₃×C₃₀₇ #37527776

order	23025
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₀₇ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²⋊C₃×C₃₀₇
unambiguous semidirect product	C₅²⋊(C₃×C₃₀₇)

Fitting, socle, Hall	C₅²×C₃₀₇ ⋊ C₃
derived, Sylow	C₅² ⋊ C₃×C₃₀₇

	subgroup	G/H
center, hypercenter	C₃₀₇	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₃×C₃₀₇
Frattini	C₁	G
Fitting, socle	C₅²×C₃₀₇	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃₀₇

12 conjugacy classes of subgroups.

μ_t(G) = 4605

3377 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23025, 4);