Finite Group Databasebeta

C9×#5048 #13142868

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

Aliases

direct productC9×#5048

Splittings

FittingC3×C9×C22⋊Q8 ⋊ C2
SylowC3×C9 ⋊ #465

Subgroups

subgroupG/H
centerC22×C9C2×#67
commutatorC2×C3×C4C23×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×C22⋊Q8C2
socleC22×C32C2×C3×D4
prime radicalC3×#930C2×C3
cosocleC2×C32×C4C23×C3
hypercenterC9×C22⋊Q8D3
hypocenterC3C9×#465
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C9 ◁ C22×C4×C9 ◁ C9×C22⋊Q8

446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8931);