C₂×C₅×C₁₁×C₃⋊D₃×C₁₉ #49178786

order	37620
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₁×C₁₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₅×C₁₁×C₃⋊D₃×C₁₉
unambiguous semidirect product	(C₂×C₃)⋊(C₅×D₃×C₁₁×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁×C₁₉	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₅×C₁₁×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₁×C₁₉	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₅×C₁₁×C₁₉

240 conjugacy classes of subgroups.

μ_t(G) = 18810

12540 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 495);