Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×C61⋊C5 |
| unambiguous semidirect product | C22⋊(C32×C61⋊C5) |
| unambiguous semidirect product | (C22×C3)⋊(C3×C61⋊C5) |
| unambiguous semidirect product | (C3×A4×C61)⋊C5 |
| Fitting, socle | C22×C3×C61 ⋊ C3×C5 |
| derived, Hall | C22×C61 ⋊ C32×C5 |
| Hall | C3×A4×C61 ⋊ C5 |
| Hall | C22×C61⋊C5 ⋊ C32 |
| Sylow | C61 ⋊ C3×C5×A4 |
| Sylow | C22 ⋊ C32×C61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×C61⋊C5 |
| commutator, cosocle, hypocenter | C22×C61 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C61 | C3×C5 |
| LCS | G ▷ C22×C61 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 122);