Finite Group Databasebeta

C9×#5005 #13142687

order1728
automorphism?
homologyAbelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23

Aliases

direct productC9×#5005

Splittings

FittingC3×C9×#117 ⋊ C2
SylowC3×C9 ⋊ #421

Subgroups

subgroupG/H
centerC4×C9C2×D12
commutatorC3×C4C22×C4×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#117C2
socleC2×C32C2×C3×C22⋊C4
prime radicalC2×C3×#235C2×C3
cosocleC2×C32×C4C23×C3
hypercenterC9×#117D3
hypocenterC3C9×#421
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C9 ◁ C22×C4×C9 ◁ C9×#117

538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8750);