Finite Group DatabasebetaFinite Group Databasebeta| order | 8019 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×#10624496 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C11 | #6862 |
| commutator, Frattini | C34 | C32×C11 |
| LCS | G ▷ C34 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C11 ◁ C33×C11 ◁ C34×C11 ◁ G | |
106 conjugacy classes of subgroups.
451 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8019, 56);