Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C11⋊C5×#509 |
| Fitting, Hall | C11×#509 ⋊ C5 |
| Sylow | C11 ⋊ C5×#509 |
180 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #509×AGL(1,𝔽11), C11⋊C5×AGL(1,ℤ/16), #72248787 |
| maximal normal subgroup of | #509×AGL(1,𝔽11), C11⋊C5×AGL(1,ℤ/16), #72248787 |
Past the SmallGroups library coverage — no SmallGroups id.