C₇×C₁₁×C₁₉×ΓL(1,𝔽₈) #44502174

order	30723
automorphism	?
homology	Abelianization (H₁) = C₃×C₇×C₁₁×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₁×C₁₉×ΓL(1,𝔽₈)
unambiguous semidirect product	C₇⋊(C₃×C₇×C₁₁×C₁₉)
unambiguous semidirect product	(C₇×C₁₁)⋊(C₃×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₇×C₁₁×C₁₉	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₃×C₇×C₁₁×C₁₉
Frattini	C₁	G
Fitting, socle	C₇²×C₁₁×C₁₉	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₇×C₁₁×C₁₉

40 conjugacy classes of subgroups.

μ_t(G) = 4389

7315 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30723, 8);