Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | SD16×D53 |
| Fitting | SD16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×SD16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD16×D53, #135×D53, AGL(1,ℤ/8)×D53, … |
| maximal normal subgroup of | C2×SD16×D53, #135×D53, AGL(1,ℤ/8)×D53, … |
| maximal quotient of | #102×D53, #103×D53, #106×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 158);