Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#6923⋊C5 |
| unambiguous semidirect product | (C9×#6923)⋊C5 |
| Fitting, Hall | C9×C61 ⋊ C4×C5 |
| derived, Sylow | C61 ⋊ C4×C5×C9 |
| Hall | C9×C61⋊C5 ⋊ C4 |
| Hall | C9×#6923 ⋊ C5 |
| Hall | C61⋊C5 ⋊ C4×C9 |
| Hall | #6923 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #6923⋊C5 |
| commutator, hypocenter | C61 | C4×C5×C9 |
| Frattini | C3 | C3×#6923⋊C5 |
| Fitting | C9×C61 | C4×C5 |
| socle | C3×C61 | C3×C4×C5 |
| prime radical | C3×D61⋊C5 | C2×C3 |
| cosocle | C3×D61 | C2×C3×C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 22);