Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D245 |
| unambiguous semidirect product | (C5×D11)⋊D49 |
| unambiguous semidirect product | (D11×C49)⋊D5 |
| Fitting, derived, Hall | C5×C11×C49 ⋊ C22 |
| Hall | C11×C49 ⋊ C2×D5 |
| Hall | C5×C49 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D49 |
| Sylow | C49 ⋊ D5×D11 |
| Sylow | C11 ⋊ C2×D245 |
| Sylow | C5 ⋊ D11×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C11×C49 | C22 |
| Frattini | C7 | D11×D35 |
| socle | C5×C7×C11 | C2×D7 |
| LCS | G ▷ C5×C11×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
868 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C5⋊(D49⋊C3), C3×D11×D245, D11×D735, … |
| maximal normal subgroup of | D11×C5⋊(D49⋊C3), C3×D11×D245 |
| maximal quotient of | C3×D11×D245, D11×D735, D33×D245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 25);