Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#11927415 |
| Fitting, Hall | C5×C9×C61 ⋊ C4 |
| derived, Hall | C5×C61 ⋊ C4×C9 |
| Hall | C9×C61 ⋊ Dic5 |
| Sylow | C61 ⋊ C9×Dic5 |
| Hall | C5×C9 ⋊ #6923 |
| Sylow | C5 ⋊ C9×#6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #11927415 |
| commutator, hypocenter | C5×C61 | C4×C9 |
| Frattini | C3 | C3×#11927415 |
| Fitting | C5×C9×C61 | C4 |
| socle | C3×C5×C61 | C3×C4 |
| prime radical, cosocle | C3×C5×D61 | C2×C3 |
| LCS | G ▷ C5×C61 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
747 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 47);