Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C49 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D11×C49 |
| Fitting | C2×C5×C11×C49 ⋊ C2 |
| derived, Sylow | C11 ⋊ C22×C5×C49 |
| Hall | C5×C11×C49 ⋊ C22 |
| Hall | C11×C49 ⋊ C22×C5 |
| Hall | C5×C11 ⋊ C22×C49 |
60 conjugacy classes of subgroups.
3430 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×D11×C49⋊C3, C5×D3×D11×C49, C2×C3×C5×D11×C49, … |
| maximal normal subgroup of | C2×C5×D11×C49⋊C3, C2×C3×C5×D11×C49 |
| maximal quotient of | C5×D3×D11×C49, C2×C3×C5×D11×C49, C2×C5×C49×D33 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 30);