Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #481 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|c^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^88,e^c=ef,g^c=g^88899 conjugacy classes — view the full character table.
| maximal subgroup of | #26019273, #26019274, #26019285, … |
| maximal normal subgroup of | #26019273, #26019274, #26019285, … |
| maximal quotient of | #26020343, #26020447, #26020567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 868);