A₄×C₁₉×C₁₃₁ #44469342

order	29868
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₉×C₁₃₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	A₄×C₁₉×C₁₃₁
unambiguous semidirect product	C₂²⋊(C₃×C₁₉×C₁₃₁)
unambiguous semidirect product	(C₂²×C₁₃₁)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉×C₁₃₁	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₁₉×C₁₃₁
Frattini	C₁	G
Fitting, socle	C₂²×C₁₉×C₁₃₁	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₁₉×C₁₃₁

20 conjugacy classes of subgroups.

μ_t(G) = 9956

9956 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29868, 25);