Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C4⋊Q8×D25 |
| Fitting | C25×C4⋊Q8 ⋊ C2 |
| Sylow | C25 ⋊ C2×C4⋊Q8 |
435 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 435 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1399);