Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×Q8×D20 |
| Fitting | C4×C52×Q8 ⋊ C2 |
| Sylow | C52 ⋊ D4×Q8 |
630 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 246 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
325 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9081);