Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(Dic61⋊C5) |
| unambiguous semidirect product | Dic549⋊C5 |
| derived, Hall | C9×C61 ⋊ C4×C5 |
| Hall | C9×C61⋊C5 ⋊ C4 |
| Hall | Dic549 ⋊ C5 |
| Hall | C61⋊C5 ⋊ Dic9 |
| Sylow | C61 ⋊ C5×Dic9 |
| Sylow | C9 ⋊ Dic61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C9⋊(D61⋊C5) |
| commutator, hypocenter | C9×C61 | C4×C5 |
| Frattini | C2×C3 | C3⋊(D61⋊C5) |
| Fitting, cosocle | C2×C9×C61 | C2×C5 |
| socle | C2×C3×C61 | C5×D3 |
| prime radical | C2×C3×C61⋊C5 | D3 |
| LCS | G ▷ C9×C61 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3,61,2,3|a^2=e,c^3=f^2,c^a=c^2f,d^a=d^60,f^a=f^2,d^b=d^9168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 6);