C₁₁⋊(C₁₉⋊#4379) #49178656

order	37620
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product	C₁₁⋊(C₁₉⋊#4379)
unambiguous semidirect product	C₁₉⋊(C₁₁⋊#4379)

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₁₁×C₁₉	C₄
prime radical, cosocle	C₅×C₁₁×C₃⋊D₃×C₁₉	C₂
LCS	G ▷ C₃²×C₅×C₁₁×C₁₉
UCS	C₁

80 conjugacy classes of subgroups.

μ_t(G) = 6270

Polycyclic presentation:

2^2,3^2,5,11,19|a^2=b,c^a=cd,d^a=cd^2,e^a=e^4,f^a=f^10,g^a=g^18,c^b=c^2,d^b=d^2

3138 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 365);