C₃×ΓL(1,𝔽₈)×C₃₁₁ #34086664

order	19593
automorphism	?
homology	Abelianization (H₁) = C₃²×C₃₁₁ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×ΓL(1,𝔽₈)×C₃₁₁
unambiguous semidirect product	C₇⋊(C₃²×C₃₁₁)
unambiguous semidirect product	(C₃×C₇)⋊(C₃×C₃₁₁)
unambiguous semidirect product	(C₇×C₃₁₁)⋊C₃²
unambiguous semidirect product	(C₃×C₇×C₃₁₁)⋊C₃

	subgroup	G/H
center, hypercenter	C₃×C₃₁₁	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₃²×C₃₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₃₁₁	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₃₁₁

24 conjugacy classes of subgroups.

μ_t(G) = 6531

4665 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19593, 4);