C₃⋊#27130977 #49137801

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

Aliases

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

288 conjugacy classes of subgroups.

μ_t(G) = 1650

Polycyclic presentation:

2^2,3,5^2,11^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^8g^8,g^a=f^7g^3,d^b=d^4,e^b=e^4,f^b=f^10,g^b=g^10

2274 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 937);