Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×SD16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #492 |
142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,89|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^c=g^88638 conjugacy classes — view the full character table.
| maximal subgroup of | #492×D89, C2×#19151969, #26030676, … |
| maximal normal subgroup of | #492×D89, C2×#19151969, #26030676, … |
| maximal quotient of | #26019838, #26019840, #26019842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 920);