Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| direct product | A5×C61⋊C3 |
| unambiguous semidirect product | C61⋊(C3×A5) |
| unambiguous semidirect product | (A5×C61)⋊C3 |
| Fitting, Sylow | C61 ⋊ C3×A5 |
| socle, derived | A5×C61 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | A5×C61 | C3 |
| Fitting, cosocle | C61 | C3×A5 |
| LCS | G ▷ A5×C61 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
115 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 222);