C₁₃×C₁₉×C₃⋊AGL(1,𝔽₇) #44527922

order	31122
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₁₉×C₃⋊AGL(1,𝔽₇)
unambiguous semidirect product	C₃⋊(C₁₃×C₁₉×AGL(1,𝔽₇))
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(D₃×C₁₃×C₁₉)
unambiguous semidirect product	D₂₁⋊(C₃×C₁₃×C₁₉)

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

72 conjugacy classes of subgroups.

μ_t(G) = 5187

2964 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 405);