Finite Group DatabasebetaFinite Group DatabasebetaOrder 10719.
8 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C9×C397 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×C397 | C9 | 1 | 1 | yes | characteristic |
| 3 | C397 | C27 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 4 | C27 | C397 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 5 | C9 | C3×C397 | 1 | 1 | yes | characteristic |
| 6 | C3 | C9×C397 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C9 | C3×C397 |
| socle, prime radical | C3×C397 | C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C397 | C27 | direct (N × H) |
| 4. C27 | C397 | direct (N × H) |