Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (Dic61⋊C5)⋊C9 |
| unambiguous semidirect product | (Dic61⋊C9)⋊C5 |
| derived, Sylow | C61 ⋊ C4×C5×C9 |
| Hall | (C61⋊C5)⋊C9 ⋊ C4 |
| Hall | Dic61⋊C9 ⋊ C5 |
| Hall | Dic61⋊C5 ⋊ C9 |
| Hall | C61⋊C9 ⋊ C4×C5 |
| Hall | C61⋊C5 ⋊ C4×C9 |
| Hall | Dic61 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | (D61⋊C3)⋊C5 |
| commutator, hypocenter | C61 | C4×C5×C9 |
| Fitting, socle, cosocle | C2×C3×C61 | C2×C3×C5 |
| prime radical | C2×C3×C61⋊C5 | C2×C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,61,2,3|a^2=e,b^3=f,d^a=d^60,d^b=d^47,d^c=d^20192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 2);