C₂×C₃×C₁₃×C₁₉×ΓL(1,𝔽₈) #44528014

order	31122
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₃×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₂×C₃×C₁₃×C₁₉×ΓL(1,𝔽₈)
unambiguous semidirect product	(C₂×C₇)⋊(C₃²×C₁₃×C₁₉)
unambiguous semidirect product	(C₂×C₃×C₇)⋊(C₃×C₁₃×C₁₉)

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

96 conjugacy classes of subgroups.

μ_t(G) = 10374

7410 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 497);