C₃×C₁₉×ΓL(1,𝔽₈) #11924784

order	1197
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₁₉×ΓL(1,𝔽₈)
unambiguous semidirect product	C₇⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₃×C₇)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₃×C₁₉	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₉	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₉

24 conjugacy classes of subgroups.

μ_t(G) = 399

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1197, 11);