Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C5×C22⋊(C61⋊C9) |
| unambiguous semidirect product | C22⋊(C5×C61⋊C9) |
| unambiguous semidirect product | (C22×C5)⋊(C61⋊C9) |
| unambiguous semidirect product | (C5×C61)⋊(C22⋊C9) |
| derived, Hall | C22×C61 ⋊ C5×C9 |
| Hall | C22×C5×C61 ⋊ C9 |
| Hall | C5×C61 ⋊ C22⋊C9 |
| Sylow | C61 ⋊ C5×C22⋊C9 |
| Hall | C22×C5 ⋊ C61⋊C9 |
| Sylow | C22 ⋊ C5×C61⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C22⋊(C61⋊C3) |
| commutator, hypocenter | C22×C61 | C5×C9 |
| Frattini | C3 | C5×C22⋊(C61⋊C3) |
| Fitting, socle, prime radical | C22×C3×C5×C61 | C3 |
| cosocle | C22×C3×C61 | C3×C5 |
| LCS | G ▷ C22×C61 | |
| UCS | C1 ◁ C3×C5 | |
32 conjugacy classes of subgroups.
1260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 63);