Finite Group DatabasebetaFinite Group Databasebeta| order | 7480 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C8 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×#3633 |
| Fitting, socle, derived, Hall | C11×C17 ⋊ C5×C8 |
| Hall | C11×#3633 ⋊ C5 |
| Hall | C17×C11⋊C5 ⋊ C8 |
| Sylow | C17 ⋊ C8×C11⋊C5 |
| Sylow | C11 ⋊ C5×#3633 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C17 | C5×C8 |
| prime radical | D17×C11⋊C5 | C4 |
| cosocle | C11×#595 | C2×C5 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 187 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊C5×AGL(1,𝔽17), AGL(1,𝔽11)×#3633, #72249058 |
| maximal normal subgroup of | C11⋊C5×AGL(1,𝔽17), AGL(1,𝔽11)×#3633, #72249058 |
Past the SmallGroups library coverage — no SmallGroups id.