C₃×C₁₃×C₁₉×AGL(1,𝔽₇) #44527827

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

Aliases

direct product	C₃×C₁₃×C₁₉×AGL(1,𝔽₇)
unambiguous semidirect product	D₇⋊(C₃²×C₁₃×C₁₉)
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₂×C₃×C₁₃×C₁₉)
unambiguous semidirect product	(C₃×D₇)⋊(C₃×C₁₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₁₉	AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₇	C₂×C₃²×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₃×C₁₉

96 conjugacy classes of subgroups.

μ_t(G) = 5187

5187 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 310);