Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #101×C509 ⋊ C2 |
| Sylow | C509 ⋊ #454 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8144 |
Polycyclic presentation:
2^6,509|c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^508,d^b=df,e^b=ef,g^b=g^508,d^c=df2810 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 724);