Finite Group DatabasebetaFinite Group Databasebeta| order | 8019 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AΣL(1,𝔽27) |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C11 · Schur multiplier (H2) = C36 |
| direct product | C32×C11×AΣL(1,𝔽27) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C11 | H(3,𝔽3) |
| commutator, Frattini | C32 | C34×C11 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C33×C11 ◁ C34×C11 ◁ G | |
2672 conjugacy classes of subgroups; only the 512 normal subgroups are shown.
This group has 2672 conjugacy classes of subgroups — too many to draw. Only its 512 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1683 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8019, 479);