Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C509 ⋊ C4 |
| Sylow | C509 ⋊ #441 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8144 |
Polycyclic presentation:
2^6,509|a^2=e,b^2=f,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^208,d^b=df,g^c=g^301,g^e=g^508911 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 1589);