C₉⋊(C₁₉⋊#1043) #30685594

order	17100
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₉⋊(C₁₉⋊#1043)
unambiguous semidirect product	C₁₉⋊(C₉⋊#1043)

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅²×C₉×C₁₉	C₄
Frattini	C₃	C₃⋊(C₁₉⋊#1043)
socle	C₃×C₅²×C₁₉	Dic₃
prime radical	C₃×C₁₉×C₅⋊D₅	D₃
cosocle	C₉×C₁₉×C₅⋊D₅	C₂
LCS	G ▷ C₅²×C₉×C₁₉
UCS	C₁

144 conjugacy classes of subgroups.

μ_t(G) = 4275

Polycyclic presentation:

2^2,3,5^2,19,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^2,e^a=e^2,f^a=f^18,g^a=g^2,d^b=d^4,e^b=e^4

1200 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 231);