C₂²⋊(C₃₃₁⋊C₉) #26045551

order	11916
automorphism	?
homology	Abelianization (H₁) = C₉ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	C₂²⋊(C₃₃₁⋊C₉)
unambiguous semidirect product	C₃₃₁⋊(C₂²⋊C₉)

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₂²⋊(C₃₃₁⋊C₃)
commutator, hypocenter	C₂²×C₃₃₁	C₉
Fitting, socle, prime radical, cosocle	C₂²×C₃×C₃₃₁	C₃
LCS	G ▷ C₂²×C₃₃₁
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Polycyclic presentation:

3,2^2,331,3|a^3=e,b^a=c,c^a=bc,d^a=d^299

1332 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11916, 12);