Finite Group DatabasebetaFinite Group Databasebeta| order | 5985 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#11924777 |
| derived, Hall | C7×C19 ⋊ C5×C9 |
| Hall | C5×C7×C19 ⋊ C9 |
| Hall | C5×C19 ⋊ C7⋊C9 |
| Hall | C5×C7 ⋊ #4294 |
| Sylow | C19 ⋊ C5×C7⋊C9 |
| Sylow | C7 ⋊ C5×#4294 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #87705 |
| commutator, hypocenter | C7×C19 | C5×C9 |
| Frattini | C3 | C5×#87705 |
| Fitting, socle | C3×C5×C7×C19 | C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
705 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5985, 4);