C₉⋊(C₁₉⋊#5997) #45691687

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₇

Aliases

unambiguous semidirect product	C₉⋊(C₁₉⋊#5997)
unambiguous semidirect product	C₁₉⋊(C₉⋊#5997)

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₇²×C₉×C₁₉	C₄
Frattini	C₃	C₃⋊(C₁₉⋊#5997)
socle	C₃×C₇²×C₁₉	Dic₃
prime radical	C₃×C₁₉×C₇⋊D₇	D₃
cosocle	C₉×C₁₉×C₇⋊D₇	C₂
LCS	G ▷ C₇²×C₉×C₁₉
UCS	C₁

84 conjugacy classes of subgroups.

μ_t(G) = 2394

Polycyclic presentation:

2^2,3,7^2,19,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^4e^6,e^a=d^3e^3,f^a=f^18,g^a=g^2,d^b=d^6,e^b=e^6

2226 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 485);