Finite Group DatabasebetaFinite Group Databasebeta| order | 8019 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C11 · Schur multiplier (H2) = C32 |
| direct product | C11×#10624677 |
| 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 ◁ C32×C9×C11 ◁ G | |
198 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
451 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8019, 237);