Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D11×D49 |
| Fitting, Hall | C5×C11×C49 ⋊ C22 |
| derived, Hall | C11×C49 ⋊ C22×C5 |
| Hall | C5×C49 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×C5×D11 |
| Sylow | C11 ⋊ C2×C5×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D11×D49 |
| commutator, cosocle, hypocenter | C11×C49 | C22×C5 |
| Frattini | C7 | C5×D7×D11 |
| Fitting | C5×C11×C49 | C22 |
| socle | C5×C7×C11 | C2×D7 |
| LCS | G ▷ C11×C49 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
910 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D11×D49⋊C3, C3×C5×D11×D49, C5×D11×D147, … |
| maximal normal subgroup of | C5×D11×D49⋊C3, C3×C5×D11×D49 |
| maximal quotient of | C3×C5×D11×D49, C5×D11×D147, C5×D33×D49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 23);