C₉⋊#16809980 #44477443

order	30420
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₉×C₁₆₉	C₄
Frattini	C₃×C₁₃	C₃⋊#63121
socle	C₃×C₅×C₁₃	C₃⋊#261
prime radical	C₃×D₈₄₅	D₃
cosocle	C₉×D₈₄₅	C₂
LCS	G ▷ C₅×C₉×C₁₆₉
UCS	C₁

54 conjugacy classes of subgroups.

μ_t(G) = 7605

Polycyclic presentation:

2^2,3,5,13,3,13|a^2=b,c^3=f^2,e^13=g^8,c^a=c^2f,d^a=d^3,e^a=e^5g,f^a=f^2,g^a=g^5,d^b=d^4,e^b=e^12g^5,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, 32);