Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#15668040 |
| Fitting | C2×M16×C89 ⋊ C2 |
| Sylow | C89 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
902 conjugacy classes — view the full character table.
| maximal subgroup of | #26020627, #26020629, #26020731, … |
| maximal normal subgroup of | #26020627, #26020629, #26020731, … |
| maximal quotient of | C2×#19151604, C2×#19151600, C2×#19151640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 1338);