Finite Group DatabasebetaFinite Group Databasebeta| order | 9477 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9×C13 · Schur multiplier (H2) = C33 |
| direct product | C13×AΣL(1,𝔽27)⋊C9 |
| unambiguous semidirect product | AΣL(1,𝔽27)⋊(C9×C13) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C13 | C3×H(3,𝔽3) |
| commutator | C32 | C32×C9×C13 |
| Frattini, cosocle | C33 | C33×C13 |
| prime radical | C3×C13×AΣL(1,𝔽27) | C3 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C13 ◁ C32×C9×C13 ◁ G | |
304 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1365 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9477, 280);