Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C89 ⋊ #485 |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|a^2=f,b^2=f,c^2=d,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 | #485×D89, C2×#19151940, #26030164, … |
| maximal normal subgroup of | #485×D89, C2×#19151940, #26030164, … |
| maximal quotient of | #26020348, #26020453, #26020562, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 891);