C₆₇×C₁₂₇⋊C₃ #38784255

order	25527
automorphism	?
homology	Abelianization (H₁) = C₃×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₆₇×C₁₂₇⋊C₃
unambiguous semidirect product	C₁₂₇⋊(C₃×C₆₇)

Fitting, socle, Hall	C₆₇×C₁₂₇ ⋊ C₃
derived, Sylow	C₁₂₇ ⋊ C₃×C₆₇

	subgroup	G/H
center, hypercenter	C₆₇	C₁₂₇⋊C₃
commutator, cosocle, hypocenter	C₁₂₇	C₃×C₆₇
Frattini	C₁	G
Fitting, socle	C₆₇×C₁₂₇	C₃
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₆₇

8 conjugacy classes of subgroups.

μ_t(G) = 8509

3015 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25527, 2);