Finite Group DatabasebetaFinite Group DatabasebetaOrder 10769.
6 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C11×C89 | C11 | 1 | 1 | yes | maximal, characteristic |
| 2 | C121 | — | 89 | 1 | no | maximal, Sylow |
| 3 | C89 | C121 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 4 | C11 | C89⋊C11 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C11 | C89⋊C11 |
| commutator, hypocenter | C89 | C121 |
| Fitting, socle, prime radical, cosocle | C11×C89 | C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C11 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C89 | C121 | semidirect |