C₂×C₁₉×ΓL(1,𝔽₈)×C₄₃ #46804875

order	34314
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₉×ΓL(1,𝔽₈)×C₄₃
unambiguous semidirect product	(C₂×C₇)⋊(C₃×C₁₉×C₄₃)

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₄₃	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₁₉×C₄₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₉×C₄₃	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₁₉×C₄₃

32 conjugacy classes of subgroups.

μ_t(G) = 11438

8170 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34314, 7);