Finite Group DatabasebetaFinite Group DatabasebetaOrder 10756.
6 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C2689 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2689 | C4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 3 | C4 | — | 2689 | 1 | no | maximal, Sylow |
| 4 | C2 | D2689 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2689 |
| commutator, hypocenter | C2689 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C2689 | C2 |
| LCS | G ▷ C2689 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2689 | C4 | semidirect |