Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D7×D77 |
| unambiguous semidirect product | (C7×D7)⋊(C5×D11) |
| Fitting, socle, Hall | C5×C72×C11 ⋊ C22 |
| derived, Hall | C72×C11 ⋊ C22×C5 |
| Hall | C5×C72 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ D72 |
| Sylow | C72 ⋊ C2×C5×D11 |
| Sylow | C11 ⋊ C5×D72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D7×D77 |
| commutator, cosocle, hypocenter | C72×C11 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | C22 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C5 | |
104 conjugacy classes of subgroups.
1000 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 72);