Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C5 |
| direct product | C2×#13103058 |
| Fitting | C2×C52×#135 ⋊ C2 |
| Sylow | C52 ⋊ C2×#509 |
1600 conjugacy classes of subgroups; only the 379 normal subgroups are shown.
This group has 1600 conjugacy classes of subgroups — too many to draw. Only its 379 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
368 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5⋊D5×#509 |
| maximal normal subgroup of | C2×C5⋊D5×#509 |
Past the SmallGroups library coverage — no SmallGroups id.