Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q8×C509 ⋊ C2 |
| Sylow | C509 ⋊ #520 |
294 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16288 |
Polycyclic presentation:
2^6,509|a^2=f,d^2=e,b^a=be,d^a=de,c^b=ce,g^b=g^508,g^c=g^508,g^d=g^5085114 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 1031);