Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of AΓL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×AΓL(1,𝔽9) |
| unambiguous semidirect product | AGL(1,𝔽9)⋊C24 |
| unambiguous semidirect product | PSU(3,𝔽2)⋊C24 |
| Fitting, socle | C23×C32 ⋊ SD16 |
| Sylow | C32 ⋊ C23×SD16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | AΓL(1,𝔽9) |
| commutator, cosocle | #157 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C23×C32 | SD16 |
| prime radical | C23×GO+(4,𝔽2) | C2 |
| hypocenter | C32 | C23×SD16 |
| LCS | G ▷ #157 ▷ C3⋊D3 ▷ C32 | |
| UCS | C1 ◁ C23 | |
2094 conjugacy classes of subgroups; only the 492 normal subgroups are shown.
This group has 2094 conjugacy classes of subgroups — too many to draw. Only its 492 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152581);