Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #100×#1035 |
| Fitting | C25×#100 ⋊ C4 |
| Sylow | C25 ⋊ C4×#100 |
540 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 540 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) = 200 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | #453×#1035, #100×AGL(1,ℤ/25) |
| maximal normal subgroup of | #453×#1035, #100×AGL(1,ℤ/25) |
Past the SmallGroups library coverage — no SmallGroups id.