Finite Group Databasebeta

C3×D9×#117 #13152481

order1728
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×D9×#117

Splittings

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

Subgroups

subgroupG/H
centerC2×C3×C4C22×D9
commutatorC2×C9C23×C3×C4
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#117C2
socleC22×C32C23×D3
prime radicalC23×C3×D9C22
cosocleC22×C9C24×C3
hypercenterC3×#117D9
hypocenterC9C2×C3×#117
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3×C4 ◁ C3×#117

1066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18544);