Finite Group DatabasebetaFinite Group Databasebeta| order | 6528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C22×D3×AGL(1,𝔽17) |
| Fitting, socle | C22×C3×C17 ⋊ C2×C16 |
| derived, Hall | C3×C17 ⋊ C23×C16 |
| Sylow | C17 ⋊ C22×D3×C16 |
| Sylow | C3 ⋊ C23×AGL(1,𝔽17) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×AGL(1,𝔽17) |
| commutator, hypocenter | C3×C17 | C23×C16 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C17 | C2×C16 |
| prime radical | C22×D3×D17 | C8 |
| cosocle | C3×#3633 | C24 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C22 | |
880 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 290 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 204 |
204 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.