Finite Group DatabasebetaFinite Group Databasebeta| order | 3392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D53⋊M32 |
| Sylow | C53 ⋊ C2×M32 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^6,53|a^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^30,g^c=g^52,g^d=g^52248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3392, 1605);