Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C2×C5×Q8×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C4×C5×Q8) |
| Fitting | C2×C52×Q8 ⋊ C4 |
| Sylow | C52 ⋊ C2×C4×Q8 |
615 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 615 conjugacy classes of subgroups — too many to draw. Only its 312 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10080);