Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C11⋊C5×D49 |
| unambiguous semidirect product | C49⋊(C22×C11⋊C5) |
| unambiguous semidirect product | (C2×C49)⋊(C2×C11⋊C5) |
| unambiguous semidirect product | (C2×C11×D49)⋊C5 |
| Fitting | C2×C11×C49 ⋊ C2×C5 |
| derived, Hall | C11×C49 ⋊ C22×C5 |
| Hall | C49×C11⋊C5 ⋊ C22 |
| Hall | C2×C11×D49 ⋊ C5 |
| Sylow | C49 ⋊ C22×C11⋊C5 |
| Sylow | C11 ⋊ C2×C5×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊C5×D49 |
| commutator, cosocle, hypocenter | C11×C49 | C22×C5 |
| Frattini | C7 | C2×D7×C11⋊C5 |
| Fitting | C2×C11×C49 | C2×C5 |
| socle | C2×C7×C11 | C5×D7 |
| LCS | G ▷ C11×C49 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
364 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C11⋊C5×D49⋊C3, D3×C11⋊C5×D49, C2×C3×C11⋊C5×D49, … |
| maximal normal subgroup of | C2×C11⋊C5×D49⋊C3, C2×C3×C11⋊C5×D49 |
| maximal quotient of | D3×C11⋊C5×D49, C2×C3×C11⋊C5×D49, C2×C11⋊C5×D147 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 16);