Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C61 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic9×C61 |
| unambiguous semidirect product | C9⋊(C4×C5×C61) |
| derived, Sylow | C9 ⋊ C4×C5×C61 |
| Hall | C5×C9×C61 ⋊ C4 |
| Hall | C9×C61 ⋊ C4×C5 |
| Hall | C5×C9 ⋊ C4×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C61 | D9 |
| commutator, hypocenter | C9 | C4×C5×C61 |
| Frattini | C2×C3 | C5×D3×C61 |
| Fitting | C2×C5×C9×C61 | C2 |
| socle, prime radical | C2×C3×C5×C61 | D3 |
| cosocle | C2×C9 | C2×C5×C61 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C5×C61 | |
36 conjugacy classes of subgroups.
3660 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 15);