Finite Group DatabasebetaFinite Group Databasebeta| order | 8019 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C11 · Schur multiplier (H2) = C33 |
| direct product | C11×#10624675 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C11 | C3×H(3,𝔽3) |
| commutator, Frattini | C33 | C33×C11 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C11 ◁ C34×C11 ◁ G | |
236 conjugacy classes of subgroups.
451 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8019, 235);