Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#11719913 |
| Fitting | C2×C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×SD16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
430 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16810710, C4×#11719913, #16810722, … |
| maximal normal subgroup of | #16810710, C4×#11719913, #16810722, … |
| maximal quotient of | C2×#13133139, C2×#13133142, C2×#13133149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 161);