ΓL(1,𝔽₈)×C₁₀₈₇ #37503764

order	22827
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₀₈₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	ΓL(1,𝔽₈)×C₁₀₈₇
unambiguous semidirect product	C₇⋊(C₃×C₁₀₈₇)

Fitting, socle, Hall	C₇×C₁₀₈₇ ⋊ C₃
derived, Sylow	C₇ ⋊ C₃×C₁₀₈₇

	subgroup	G/H
center, hypercenter	C₁₀₈₇	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₃×C₁₀₈₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₀₈₇	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₀₈₇

8 conjugacy classes of subgroups.

μ_t(G) = 7609

5435 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22827, 1);