Finite Group DatabasebetaFinite Group Databasebeta| order | 29920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C16 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽11)×AGL(1,𝔽17) |
| Fitting, socle, derived, Hall | C11×C17 ⋊ C2×C5×C16 |
| Hall | D11×AGL(1,𝔽17) ⋊ C5 |
| Hall | C17×C11⋊C5 ⋊ C2×C16 |
| Hall | C11⋊C5 ⋊ C2×AGL(1,𝔽17) |
| Sylow | C17 ⋊ C16×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C2×C5×AGL(1,𝔽17) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C17 | C2×C5×C16 |
| prime radical | D17×AGL(1,𝔽11) | C8 |
| cosocle | C11×#3633 | C22×C5 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 | |
112 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 187 |
187 conjugacy classes — view the full character table.
| holomorph of | C11×C17 |
Past the SmallGroups library coverage — no SmallGroups id.