C₁₃×AGL(1,𝔽₇)×C₁₉⋊C₃ #44527656

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

Aliases

direct product	C₁₃×AGL(1,𝔽₇)×C₁₉⋊C₃
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₂×C₁₃×C₁₉⋊C₃)
unambiguous semidirect product	(D₇×C₁₉⋊C₃)⋊(C₃×C₁₃)
unambiguous semidirect product	(C₁₉×AGL(1,𝔽₇))⋊(C₃×C₁₃)
unambiguous semidirect product	#11716325⋊(C₃×C₁₃)
unambiguous semidirect product	#11716326⋊(C₃×C₁₃)

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

96 conjugacy classes of subgroups.

μ_t(G) = 1729

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 139);