Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22×AΓL(1,𝔽25) |
| Fitting, socle | C22×C52 ⋊ ΓL(1,𝔽25) |
| Hall | C52⋊C3 ⋊ C22×M16 |
| Sylow | C52 ⋊ C22×ΓL(1,𝔽25) |
714 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 172 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 100 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | C22×AGL(2,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.