C₂×C₁₉×C₁₂₁⋊C₅ #37527352

order	22990
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₉×C₁₂₁⋊C₅
unambiguous semidirect product	(C₂×C₁₂₁)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₂×C₁₉×C₁₂₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₁₂₁⋊C₅
commutator, cosocle, hypocenter	C₁₂₁	C₂×C₅×C₁₉
Frattini	C₁₁	C₂×C₁₉×C₁₁⋊C₅
Fitting	C₂×C₁₉×C₁₂₁	C₅
socle	C₂×C₁₁×C₁₉	C₁₁⋊C₅
LCS	G ▷ C₁₂₁
UCS	C₁ ◁ C₂×C₁₉

24 conjugacy classes of subgroups.

μ_t(G) = 4598

1102 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22990, 2);