Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C22⋊C9×C61⋊C5 |
| unambiguous semidirect product | C22⋊(C9×C61⋊C5) |
| unambiguous semidirect product | (C22⋊C9×C61)⋊C5 |
| derived, Hall | C22×C61 ⋊ C5×C9 |
| Hall | C22⋊C9×C61 ⋊ C5 |
| Hall | C22×C61⋊C5 ⋊ C9 |
| Sylow | C61 ⋊ C5×C22⋊C9 |
| Sylow | C22 ⋊ C9×C61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | A4×C61⋊C5 |
| commutator, hypocenter | C22×C61 | C5×C9 |
| Fitting, socle, cosocle | C22×C3×C61 | C3×C5 |
| prime radical | C22×C3×C61⋊C5 | C3 |
| LCS | G ▷ C22×C61 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 27);