#27130981⋊C₃ #49137625

order	36300
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₅×C₁₁

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₁²	C₃×C₄
prime radical	C₅⋊(C₅⋊((C₁₁⋊D₁₁)⋊C₃))	C₂
cosocle	C₅⋊(C₅⋊(C₁₁⋊D₁₁))	C₂×C₃
LCS	G ▷ C₅²×C₁₁²
UCS	C₁

96 conjugacy classes of subgroups.

μ_t(G) = 330

Polycyclic presentation:

2,3,2,5^2,11^2|a^2=c,d^a=d^2,e^a=e^3,f^a=f^5g^7,g^a=fg^6,f^b=f^9g^10,g^b=f^3g,d^c=d^4,e^c=e^4,f^c=f^10,g^c=g^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 761);