Finite Group DatabasebetaFinite Group Databasebeta| order | 7920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C11⋊C5×#3811 |
| Fitting | C22×C32×C11 ⋊ C22×C5 |
| Hall | C11×#3811 ⋊ C5 |
| Hall | C32×C11⋊C5 ⋊ C2×D4 |
| Hall | C32×C11 ⋊ C2×C5×D4 |
| Sylow | C11 ⋊ C5×#3811 |
| Sylow | C32 ⋊ C2×D4×C11⋊C5 |
496 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 132 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×#3811 |
| maximal normal subgroup of | AGL(1,𝔽11)×#3811 |
Past the SmallGroups library coverage — no SmallGroups id.