Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #495 |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|b^2=d,c^2=ef,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^88,g^b=g^88,g^c=g^88638 conjugacy classes — view the full character table.
| maximal subgroup of | #26022309, #26022310, #26022316, … |
| maximal normal subgroup of | #26022309, #26022310, #26022316, … |
| maximal quotient of | #26019845, #26019846, #26019855, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 934);