ΓL(1,𝔽₈)×C₁₄₈₉ #44530775

order	31269
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₄₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	ΓL(1,𝔽₈)×C₁₄₈₉
unambiguous semidirect product	C₇⋊(C₃×C₁₄₈₉)

Fitting, socle, Hall	C₇×C₁₄₈₉ ⋊ C₃
derived, Sylow	C₇ ⋊ C₃×C₁₄₈₉

	subgroup	G/H
center, hypercenter	C₁₄₈₉	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₃×C₁₄₈₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₄₈₉	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₄₈₉

8 conjugacy classes of subgroups.

μ_t(G) = 10423

7445 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31269, 1);