Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#13104753 |
| Fitting | C2×C52×Q16 ⋊ C4 |
| Sylow | C52 ⋊ C2×#444 |
1856 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 1856 conjugacy classes of subgroups — too many to draw. Only its 294 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72253147 |
| maximal normal subgroup of | C2×#72253147 |
Past the SmallGroups library coverage — no SmallGroups id.