Finite Group Databasebeta

D3×C9×#117 #13152494

order1728
automorphism?
homologyAbelianization (H1) = C23×C4×C9 · Schur multiplier (H2) = C24×C4

Aliases

direct productD3×C9×#117

Splittings

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

Subgroups

subgroupG/H
centerC2×C4×C9C22×D3
commutatorC2×C3C23×C4×C9
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#117C2
socle, cosocleC22×C32C24×C3
prime radicalC23×C3×D3C22×C3
hypercenterC9×#117D3
hypocenterC3C2×C9×#117
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C9 ◁ C9×#117

1066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18557);