Finite Group DatabasebetaFinite Group Databasebeta| order | 7480 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | #595×AGL(1,𝔽11) |
| Fitting, socle, derived, Hall | C11×C17 ⋊ C2×C4×C5 |
| Hall | D11×#595 ⋊ C5 |
| Hall | C17×C11⋊C5 ⋊ C2×C4 |
| Hall | C11⋊C5 ⋊ C2×#595 |
| Sylow | C17 ⋊ C4×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C2×C5×#595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C17 | C2×C4×C5 |
| prime radical | D17×AGL(1,𝔽11) | C2 |
| cosocle | C11×D17 | C22×C5 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 187 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×#3633 |
| maximal normal subgroup of | AGL(1,𝔽11)×#3633 |
Past the SmallGroups library coverage — no SmallGroups id.