Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (#6923⋊C5)⋊C9 |
| unambiguous semidirect product | (#6923⋊C9)⋊C5 |
| derived, Sylow | C61 ⋊ C4×C5×C9 |
| Hall | (C61⋊C5)⋊C9 ⋊ C4 |
| Hall | #6923⋊C9 ⋊ C5 |
| Hall | #6923⋊C5 ⋊ C9 |
| Hall | C61⋊C9 ⋊ C4×C5 |
| Hall | C61⋊C5 ⋊ C4×C9 |
| Hall | #6923 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | AGL(1,𝔽61) |
| commutator, hypocenter | C61 | C4×C5×C9 |
| Fitting, socle | C3×C61 | C3×C4×C5 |
| prime radical | C3×D61⋊C5 | C2×C3 |
| cosocle | C3×D61 | C2×C3×C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,2,61,3|a^2=d,b^3=f,e^a=e^50,e^b=e^13,e^c=e^9,e^d=e^60183 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 20);