Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×AΓL(1,𝔽25) |
| Fitting | C4×C52 ⋊ ΓL(1,𝔽25) |
| Hall | C52⋊C3 ⋊ C4×M16 |
| Sylow | C52 ⋊ C4×ΓL(1,𝔽25) |
338 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 86 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 | C4×AGL(2,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.