Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | M32×#1043 |
| Fitting | C52×M32 ⋊ C4 |
| Sylow | C52 ⋊ C4×M32 |
784 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 784 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) = 400 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #347×#1043, #365×#1043, #509×#1043, … |
| maximal normal subgroup of | #347×#1043, #365×#1043, #509×#1043, … |
| maximal quotient of | #346×#1043, C2×M32×#1043 |
Past the SmallGroups library coverage — no SmallGroups id.