Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| derived, Hall | C5×C61 ⋊ C22×C9 |
| Hall | C5×C61⋊C9 ⋊ C22 |
| Hall | D5×D61 ⋊ C9 |
| Hall | C61⋊C9 ⋊ C2×D5 |
| Sylow | C61 ⋊ C2×C9×D5 |
| Sylow | C5 ⋊ C2×D61⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D5×D61⋊C3 |
| commutator, hypocenter | C5×C61 | C22×C9 |
| Fitting, socle, cosocle | C3×C5×C61 | C22×C3 |
| prime radical | C3×D5×D61 | C3 |
| LCS | G ▷ C5×C61 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 34);