Finite Group DatabasebetaFinite Group Databasebeta| order | 4000 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×AGL(1,ℤ/25) |
| Fitting | C8×5−1+2 ⋊ C4 |
| derived | C25 ⋊ C4×C5×C8 |
| Sylow | 5−1+2 ⋊ C4×C8 |
136 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | M16×AGL(1,ℤ/25), SD16×AGL(1,ℤ/25), D8×AGL(1,ℤ/25) |
| maximal normal subgroup of | M16×AGL(1,ℤ/25), SD16×AGL(1,ℤ/25), D8×AGL(1,ℤ/25) |
Past the SmallGroups library coverage — no SmallGroups id.