C₁₉×ΓL(1,𝔽₈)×D₃₉ #44527988

order	31122
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×ΓL(1,𝔽₈)×D₃₉
unambiguous semidirect product	C₃⋊(C₁₉×ΓL(1,𝔽₈)×D₁₃)

	subgroup	G/H
center, hypercenter	C₁₉	ΓL(1,𝔽₈)×D₃₉
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₁₉

72 conjugacy classes of subgroups.

μ_t(G) = 5187

1995 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 471);