Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C11×C49 ⋊ C22×C5 |
| Hall | C49×C11⋊C5 ⋊ C22 |
| Hall | D11×D49 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C2×C5×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C11×C49 | C22×C5 |
| Frattini | C7 | D7×AGL(1,𝔽11) |
| socle | C7×C11 | C2×C5×D7 |
| LCS | G ▷ C11×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 14);