Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C433 ⋊ #349 |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6928 |
Polycyclic presentation:
2^6,433|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^354,d^b=df,g^b=g^432,g^d=g^179,g^e=g^432454 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1648);