C₃⋊(C₃⋊#16809980) #44477535

order	30420
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₃²×C₅×C₁₆₉	C₄
Frattini	C₁₃	C₃⋊(C₃⋊#63121)
socle	C₃²×C₅×C₁₃	#261
prime radical, cosocle	C₃²×D₈₄₅	C₂
LCS	G ▷ C₃²×C₅×C₁₆₉
UCS	C₁

108 conjugacy classes of subgroups.

μ_t(G) = 7605

Polycyclic presentation:

2^2,3^2,5,13^2|a^2=b,f^13=g^2,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^8g,g^a=g^8,e^b=e^4,f^b=f^12g^11,g^b=g^12

1911 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 124);