C₃⋊#27130906 #49137440

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

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₃×C₅×#10597245	C₄
Fitting, socle	C₃×C₅×C₁₁²	Dic₅
prime radical, cosocle	C₃×C₅⋊#11925893	C₂
LCS	G ▷ C₃×C₅×#10597245
UCS	C₁

80 conjugacy classes of subgroups.

μ_t(G) = 330

Polycyclic presentation:

2^2,3,5^2,11^2|a^2=b,c^a=c^2,d^a=d^4,e^a=e^2,f^a=f^7g^8,g^a=f^2g^4,e^b=e^4,f^b=f^10,g^b=g^10,f^d=f^3g^9,g^d=g^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 576);