Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C8×#1043 |
| Fitting | C52×C22⋊C8 ⋊ C4 |
| Sylow | C52 ⋊ C4×C22⋊C8 |
1744 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1744 conjugacy classes of subgroups — too many to draw. Only its 232 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 | C8×D4×#1043 |
| maximal normal subgroup of | C8×D4×#1043 |
| maximal quotient of | D4⋊C8×#1043 |
Past the SmallGroups library coverage — no SmallGroups id.