Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D49×D55 |
| unambiguous semidirect product | (C5×D49)⋊D11 |
| unambiguous semidirect product | (C11×D49)⋊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 ⋊ C2×D55 |
| Sylow | C11 ⋊ D5×D49 |
| Sylow | C5 ⋊ D11×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C11×C49 | C22 |
| Frattini | C7 | D7×D55 |
| socle | C5×C7×C11 | C2×D7 |
| LCS | G ▷ C5×C11×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
754 conjugacy classes — view the full character table.
| maximal subgroup of | D55×D49⋊C3, C3×D49×D55, D49×D165, … |
| maximal normal subgroup of | D55×D49⋊C3, C3×D49×D55 |
| maximal quotient of | C3×D49×D55, D49×D165, D55×D147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 27);