C₂×C₁₉×ΓL(1,𝔽₈)×C₁₃⋊C₃ #44527806

order	31122
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₂×C₁₉×ΓL(1,𝔽₈)×C₁₃⋊C₃
unambiguous semidirect product	(C₂×C₇×C₁₃⋊C₃)⋊(C₃×C₁₉)
unambiguous semidirect product	(C₂×C₁₃×ΓL(1,𝔽₈))⋊(C₃×C₁₉)
unambiguous semidirect product	(C₂×#63270)⋊(C₃×C₁₉)
unambiguous semidirect product	(C₂×#63271)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₁₉	ΓL(1,𝔽₈)×C₁₃⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃×C₁₉	C₃²
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₁₉

96 conjugacy classes of subgroups.

μ_t(G) = 3458

1330 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 289);