C₃⋊(C₃⋊#16814854) #45685894

order	33300
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₃²×C₂₅×C₃₇	C₄
Frattini	C₅	C₃⋊(C₃⋊#10625191)
socle	C₃²×C₅×C₃₇	AGL(1,𝔽₅)
prime radical, cosocle	C₃²×D₉₂₅	C₂
LCS	G ▷ C₃²×C₂₅×C₃₇
UCS	C₁

108 conjugacy classes of subgroups.

μ_t(G) = 8325

Polycyclic presentation:

2^2,3^2,5,37,5|a^2=b,e^5=g,c^a=c^2,d^a=d^2,e^a=e^2g,f^a=f^31,g^a=g^2,e^b=e^4g^4,f^b=f^36,g^b=g^4

2091 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 167);