C₁₁⋊(#4296⋊Dic₅) #49178447

order	37620
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₁₁⋊(#4296⋊Dic₅)
unambiguous semidirect product	#4296⋊Dic₅₅

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊(C₁₁⋊AGL(1,𝔽₁₉))
commutator, hypocenter	C₅×C₁₁×C₁₉	C₄×C₉
Fitting, socle	C₂×C₅×C₁₁×C₁₉	C₂×C₉
prime radical, cosocle	C₂×C₅×C₁₁×C₁₉⋊C₃	C₂×C₃
LCS	G ▷ C₅×C₁₁×C₁₉
UCS	C₁ ◁ C₂

72 conjugacy classes of subgroups.

μ_t(G) = 4180

Polycyclic presentation:

2,3^2,5,11,19,2|a^2=g,b^3=c,d^a=d^4,e^a=e^10,f^a=f^18,f^b=f^4,f^c=f^7

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 156);