Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#20294109 |
| Sylow | C433 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27712 |
Polycyclic presentation:
2^6,433|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^354,g^d=g^179,g^e=g^432472 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1651);