Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D35⋊D11 |
| unambiguous semidirect product | D35⋊(C7×D11) |
| unambiguous semidirect product | D55⋊(C7×D7) |
| unambiguous semidirect product | D77⋊(C7×D5) |
| Fitting, socle, Hall | C5×C72×C11 ⋊ C22 |
| derived | C5×C7×C11 ⋊ C22×C7 |
| Hall | C72×C11 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ D5×D11 |
| Sylow | C11 ⋊ C7×D5×D7 |
| Sylow | C5 ⋊ C7×D7×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D35⋊D11 |
| commutator, cosocle, hypocenter | C5×C7×C11 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | C22 |
| LCS | G ▷ C5×C7×C11 | |
| UCS | C1 ◁ C7 | |
104 conjugacy classes of subgroups.
805 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 89);