Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4×C5 |
| direct product | C5⋊D5×#493 |
| Fitting | C52×#493 ⋊ C2 |
| Sylow | C52 ⋊ C2×#493 |
3040 conjugacy classes of subgroups; only the 363 normal subgroups are shown.
This group has 3040 conjugacy classes of subgroups — too many to draw. Only its 363 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #493×#1043, C5⋊D5×#3151, #72220996, … |
| maximal normal subgroup of | #493×#1043, C5⋊D5×#3151, #72220996, … |
| maximal quotient of | C5⋊D5×#1712, C5⋊D5×#1721 |
Past the SmallGroups library coverage — no SmallGroups id.