Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#20294111 |
| unambiguous semidirect product | (C2×#20294111)⋊C2 |
| Fitting | C22×C433 ⋊ C16 |
| Sylow | C433 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1732 |
Polycyclic presentation:
2^6,433|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^238,g^d=g^354,g^e=g^179,g^f=g^432148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1675);