Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D8×C509 ⋊ C4 |
| Sylow | C509 ⋊ #360 |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8144 |
Polycyclic presentation:
2^6,509|a^2=d,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^301,c^b=cef,d^b=df,e^b=ef,g^d=g^508905 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 1465);