Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×D5⋊C16 |
| unambiguous semidirect product | D5⋊(C2×C5×C16) |
| derived | C5 ⋊ C22×C5×C16 |
| Sylow | C52 ⋊ C22×C16 |
207 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 207 conjugacy classes of subgroups — too many to draw. Only its 120 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, 6825);