Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×(C2×AGL(1,𝔽5))⋊Q8 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊(C5×Q8) |
| Fitting | C2×C52×Q8 ⋊ C4 |
| Sylow | C52 ⋊ #391 |
391 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 391 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6902);