Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C29 |
| direct product | C22×C5×Q8×D5 |
| Fitting | C22×C52×Q8 ⋊ C2 |
| Sylow | C52 ⋊ C23×Q8 |
1856 conjugacy classes of subgroups; only the 1006 normal subgroups are shown.
This group has 1856 conjugacy classes of subgroups — too many to draw. Only its 1006 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10214);