C₉⋊(C₃₁⋊#1044) #42124560

order	27900
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₅

Aliases

unambiguous semidirect product	C₉⋊(C₃₁⋊#1044)
unambiguous semidirect product	C₃₁⋊(C₉⋊#1044)

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅²×C₉×C₃₁	C₄
Frattini	C₃	C₃⋊(C₃₁⋊#1044)
socle	C₃×C₅²×C₃₁	Dic₃
prime radical	C₃×C₃₁×C₅⋊D₅	D₃
cosocle	C₉×C₃₁×C₅⋊D₅	C₂
LCS	G ▷ C₅²×C₉×C₃₁
UCS	C₁

96 conjugacy classes of subgroups.

Polycyclic presentation:

2^2,3,5^2,31,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^2,e^a=e^3,f^a=f^30,g^a=g^2,d^b=d^4,e^b=e^4

1956 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 307);