(C₁₁⋊C₅)⋊(Dic₁₃⋊C₉) #38787805

order	25740
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	(C₁₁⋊C₅)⋊(Dic₁₃⋊C₉)
unambiguous semidirect product	((C₁₁⋊C₅)⋊Dic₁₃)⋊C₉
unambiguous semidirect product	(C₁₁⋊(Dic₁₃⋊C₉))⋊C₅

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	(C₁₃⋊C₃)⋊AGL(1,𝔽₁₁)
commutator, hypocenter	C₁₁×C₁₃	C₄×C₅×C₉
Fitting, socle, cosocle	C₂×C₃×C₁₁×C₁₃	C₂×C₃×C₅
prime radical	C₂×C₃×C₁₃×C₁₁⋊C₅	C₂×C₃
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₂×C₃

72 conjugacy classes of subgroups.

μ_t(G) = 5148

Polycyclic presentation:

2,3,5,11,13,2,3|a^2=f,b^3=g,d^a=d^10,e^a=e^12,e^b=e^3,d^c=d^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 36);