Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(#6923⋊C5) |
| unambiguous semidirect product | (C9⋊#6923)⋊C5 |
| Fitting, derived, Hall | C9×C61 ⋊ C4×C5 |
| Hall | C9×C61⋊C5 ⋊ C4 |
| Hall | C9⋊#6923 ⋊ C5 |
| Hall | C61⋊C5 ⋊ Dic9 |
| Sylow | C61 ⋊ C5×Dic9 |
| Sylow | C9 ⋊ #6923⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C61 | C4×C5 |
| Frattini | C3 | C3⋊(#6923⋊C5) |
| socle | C3×C61 | C5×Dic3 |
| prime radical | C3×D61⋊C5 | D3 |
| cosocle | C9×D61 | C2×C5 |
| LCS | G ▷ C9×C61 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,3,61,3|a^2=c,d^3=f^2,d^a=d^2f,e^a=e^50,f^a=f^2,e^b=e^9,e^c=e^6087 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 23);