Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C3⋊#6923 |
| unambiguous semidirect product | C3⋊(C3×C5×#6923) |
| Fitting, socle, Hall | C32×C5×C61 ⋊ C4 |
| derived | C3×C61 ⋊ C3×C4×C5 |
| Hall | C32×C61 ⋊ C4×C5 |
| Hall | C5×C61 ⋊ C3×Dic3 |
| Sylow | C61 ⋊ C3×C5×Dic3 |
| Hall | C32×C5 ⋊ #6923 |
| Sylow | C32 ⋊ C5×#6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C3⋊#6923 |
| commutator, hypocenter | C3×C61 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C61 | C4 |
| prime radical | C32×C5×D61 | C2 |
| cosocle | C3×D61 | C2×C3×C5 |
| LCS | G ▷ C3×C61 | |
| UCS | C1 ◁ C3×C5 | |
56 conjugacy classes of subgroups.
765 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 163);