ΓL(1,𝔽₈)×C₅₃ #11764337

order	1113
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₃×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	ΓL(1,𝔽₈)×C₅₃
unambiguous semidirect product	C₇⋊(C₃×C₅₃)
unambiguous semidirect product	(C₇×C₅₃)⋊C₃

Fitting, socle, Hall	C₇×C₅₃ ⋊ C₃
derived, Sylow	C₇ ⋊ C₃×C₅₃

	subgroup	G/H
center, hypercenter	C₅₃	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₃×C₅₃
Frattini	C₁	G
Fitting, socle	C₇×C₅₃	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₅₃

8 conjugacy classes of subgroups.

μ_t(G) = 371

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1113, 1);