Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q16×D53 |
| Fitting | Q16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×Q16 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×D53, Q32×D53, #16811062, … |
| maximal normal subgroup of | SD32×D53, Q32×D53, #16811062, … |
| maximal quotient of | #103×D53, #107×D53, #16810715, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 162);