C₉⋊(C₁₉⋊#1035) #30685386

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

Aliases

unambiguous semidirect product	C₉⋊(C₁₉⋊#1035)
unambiguous semidirect product	C₁₉⋊(C₉⋊#1035)

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉×C₁₉×C₂₅	C₄
Frattini	C₃×C₅	C₃⋊(C₁₉⋊AGL(1,𝔽₅))
socle	C₃×C₅×C₁₉	ΓL(1,𝔽₁₆)
prime radical	C₃×C₁₉×D₂₅	D₃
cosocle	C₉×C₁₉×D₂₅	C₂
LCS	G ▷ C₉×C₁₉×C₂₅
UCS	C₁

54 conjugacy classes of subgroups.

μ_t(G) = 4275

Polycyclic presentation:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 23);