C₉⋊(C₁₉⋊#6157) #49136226

order	36252
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₉⋊(C₁₉⋊#6157)
unambiguous semidirect product	C₁₉⋊(C₉⋊#6157)

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉×C₁₉×C₅₃	C₄
Frattini	C₃	C₃⋊(C₁₉⋊#6157)
socle	C₃×C₁₉×C₅₃	Dic₃
prime radical	C₃×C₁₉×D₅₃	D₃
cosocle	C₉×C₁₉×D₅₃	C₂
LCS	G ▷ C₉×C₁₉×C₅₃
UCS	C₁

36 conjugacy classes of subgroups.

μ_t(G) = 9063

Polycyclic presentation:

2^2,3,19,53,3|a^2=b,c^3=f^2,c^a=c^2f,d^a=d^18,e^a=e^30,f^a=f^2,e^b=e^52

2397 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 25);