Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C5 |
| direct product | C2×SD32×C5⋊D5 |
| Fitting | C2×C52×SD32 ⋊ C2 |
| Sylow | C52 ⋊ C22×SD32 |
1600 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1600 conjugacy classes of subgroups — too many to draw. Only its 275 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5⋊D5×#509, C2×SD32×#1043, C2×#72242337 |
| maximal normal subgroup of | C2×C5⋊D5×#509, C2×SD32×#1043, C2×#72242337 |
Past the SmallGroups library coverage — no SmallGroups id.