Finite Group Databasebeta

C9×#5750 #13153405

order1728
automorphism?
homologyAbelianization (H1) = C23×C4×C9 · Schur multiplier (H2) = C25

Aliases

direct productC9×#5750

Splittings

FittingC3×C9×#131 ⋊ C2
SylowC3×C9 ⋊ #568

Subgroups

subgroupG/H
centerC4×C9C23×D3
commutatorC2×C3C23×C4×C9
FrattiniC3×C4C23×C3×D3
FittingC3×C9×#131C2
socleC2×C32C23×C3×C4
prime radicalC3×D3×#41C2×C3
cosocleC32×C4C24×C3
hypercenterC9×#131D3
hypocenterC3C9×#568
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C9 ◁ C9×#131

836 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19468);