C₆₁×C₁₂₇⋊C₃ #37551242

order	23241
automorphism	?
homology	Abelianization (H₁) = C₃×C₆₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₆₁×C₁₂₇⋊C₃
unambiguous semidirect product	C₁₂₇⋊(C₃×C₆₁)

Fitting, socle, Hall	C₆₁×C₁₂₇ ⋊ C₃
derived, Sylow	C₁₂₇ ⋊ C₃×C₆₁

	subgroup	G/H
center, hypercenter	C₆₁	C₁₂₇⋊C₃
commutator, cosocle, hypocenter	C₁₂₇	C₃×C₆₁
Frattini	C₁	G
Fitting, socle	C₆₁×C₁₂₇	C₃
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₆₁

8 conjugacy classes of subgroups.

μ_t(G) = 7747

2745 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23241, 2);