C₁₉×C₁₃⋊C₃×AGL(1,𝔽₇) #44527687

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

Aliases

direct product	C₁₉×C₁₃⋊C₃×AGL(1,𝔽₇)
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₂×C₁₉×C₁₃⋊C₃)
unambiguous semidirect product	(D₇×C₁₃⋊C₃)⋊(C₃×C₁₉)
unambiguous semidirect product	(C₁₃×AGL(1,𝔽₇))⋊(C₃×C₁₉)
unambiguous semidirect product	#10587720⋊(C₃×C₁₉)
unambiguous semidirect product	#10587721⋊(C₃×C₁₉)

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

96 conjugacy classes of subgroups.

μ_t(G) = 1729

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 170);