Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of AΓL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×AΓL(1,𝔽9) |
| unambiguous semidirect product | AGL(1,𝔽9)⋊(C22×C3) |
| Fitting, socle | C2×C33 ⋊ SD16 |
| Sylow | C33 ⋊ C2×SD16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | AΓL(1,𝔽9) |
| commutator, cosocle | #157 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33 | SD16 |
| prime radical | C2×C3×GO+(4,𝔽2) | C2 |
| hypocenter | C32 | C2×C3×SD16 |
| LCS | G ▷ #157 ▷ C3⋊D3 ▷ C32 | |
| UCS | C1 ◁ C2×C3 | |
178 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4682);