C₂²×C₃²×C₁₉×C₁₁⋊C₅ #49178644

order	37620
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₅×C₁₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂²×C₃²×C₁₉×C₁₁⋊C₅
unambiguous semidirect product	(C₂²×C₃²×C₁₁)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₂²×C₃²×C₁₁×C₁₉)⋊C₅

	subgroup	G/H
center, hypercenter	C₂²×C₃²×C₁₉	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₂²×C₃²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₃²×C₁₁×C₁₉	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂²×C₃²×C₁₉

240 conjugacy classes of subgroups.

μ_t(G) = 7524

4788 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 353);