Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C32×C509 ⋊ C2 |
| Sylow | C509 ⋊ SD64 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16288 |
Polycyclic presentation:
2^6,509|a^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^508,c^b=cd,d^b=de,e^b=ef,g^b=g^5088147 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 388);