Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D53⋊M16 |
| Sylow | C53 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
Polycyclic presentation:
2^5,53|a^2=d,d^2=e,b^a=be,f^a=f^30,f^c=f^52,f^d=f^52124 conjugacy classes — view the full character table.
| maximal subgroup of | #16811490, #16811492, #16811494, … |
| maximal normal subgroup of | #16811490, #16811492, #16811494, … |
| maximal quotient of | #16811582, C4×#11719940, C4×#11719936, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 231);