Finite Group DatabasebetaFinite Group Databasebeta| order | 8019 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11×C27 · Schur multiplier (H2) = C3 |
| direct product | C11×#10624462 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C11 | C9⋊C9 |
| commutator | C9 | C3×C11×C27 |
| Frattini | C92 | C32×C11 |
| LCS | G ▷ C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C11 ◁ C92×C11 ◁ G | |
72 conjugacy classes of subgroups.
1155 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8019, 22);