Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×#1035 |
| unambiguous semidirect product | D25⋊(C4×Q8) |
| Fitting | C2×Q8×C25 ⋊ C4 |
| Sylow | C25 ⋊ C2×C4×Q8 |
447 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2025);