Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #470 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|a^2=f,b^2=df,d^2=f,b^a=bd,c^a=ce,d^a=df,c^b=cf,g^c=g^88632 conjugacy classes — view the full character table.
| maximal subgroup of | #26022201, #26022470, #470×D89, … |
| maximal normal subgroup of | #26022201, #26022470, #470×D89, … |
| maximal quotient of | #26019738, #26019743, #26019772, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 804);