Finite Group DatabasebetaFinite Group Databasebeta| order | 10608 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | #595×AGL(1,𝔽13) |
| Fitting, socle, derived, Hall | C13×C17 ⋊ C3×C42 |
| Hall | #261×#595 ⋊ C3 |
| Hall | C17×C13⋊C3 ⋊ C42 |
| Hall | C13⋊C3 ⋊ C4×#595 |
| Sylow | C17 ⋊ C4×AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×C4×#595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C17 | C3×C42 |
| prime radical | D17×D13⋊C3 | C22 |
| cosocle | D13×D17 | C22×C3 |
| LCS | G ▷ C13×C17 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 221 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #3633×AGL(1,𝔽13) |
| maximal normal subgroup of | #3633×AGL(1,𝔽13) |
Past the SmallGroups library coverage — no SmallGroups id.