Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #135×C89 ⋊ C2 |
| Sylow | C89 ⋊ #509 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,d^b=de,e^b=ef,g^b=g^88632 conjugacy classes — view the full character table.
| maximal subgroup of | #26022147, #26022150, #26022198, … |
| maximal normal subgroup of | #26022147, #26022150, #26022198, … |
| maximal quotient of | #26021964, #26021967, #26022041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 984);