Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C9⋊#6923 |
| unambiguous semidirect product | C9⋊(C5×#6923) |
| Fitting, Hall | C5×C9×C61 ⋊ C4 |
| derived, Hall | C9×C61 ⋊ C4×C5 |
| Hall | C5×C61 ⋊ Dic9 |
| Sylow | C61 ⋊ C5×Dic9 |
| Hall | C5×C9 ⋊ #6923 |
| Sylow | C9 ⋊ C5×#6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C9⋊#6923 |
| commutator, hypocenter | C9×C61 | C4×C5 |
| Frattini | C3 | C5×C3⋊#6923 |
| Fitting | C5×C9×C61 | C4 |
| socle | C3×C5×C61 | Dic3 |
| prime radical | C3×C5×D61 | D3 |
| cosocle | C9×D61 | C2×C5 |
| LCS | G ▷ C9×C61 | |
| UCS | C1 ◁ C5 | |
36 conjugacy classes of subgroups.
735 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 49);