Finite Group DatabasebetaFinite Group Databasebeta| order | 8019 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C35⋊C11 |
| unambiguous semidirect product | C36⋊C11 |
| Fitting, socle, Sylow | C36 ⋊ C11 |
| derived | C35 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C35⋊C11 |
| commutator, hypocenter | C35 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C36 | C11 |
| LCS | G ▷ C35 | |
| UCS | C1 ◁ C3 | |
5156 conjugacy classes of subgroups.
99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8019, 505);