(C₁₁⋊C₅)⋊#10596868 #44568455

order	32340
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	(C₁₁⋊C₅)⋊#10596868
unambiguous semidirect product	(C₁₁⋊#10596868)⋊C₅

	subgroup	G/H
center, Frattini, hypercenter	C₂	(C₁₁⋊C₅)⋊#64418
commutator, hypocenter	C₁₁×#3862	C₄×C₅
Fitting, socle	C₂×C₇²×C₁₁	C₅×D₃
prime radical	C₂×C₁₁⋊C₅×#3862	C₂
cosocle	C₂×C₁₁×#3862	C₂×C₅
LCS	G ▷ C₁₁×#3862
UCS	C₁ ◁ C₂

88 conjugacy classes of subgroups.

μ_t(G) = 308

Polycyclic presentation:

2,5,3,11,7^2,2|a^2=g,c^a=c^2,d^a=d^10,e^a=e^2f^3,f^a=e^6f^5,d^b=d^4,e^c=e^4f^4,f^c=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 157);