Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C509 ⋊ C4 |
| Sylow | C509 ⋊ #519 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8144 |
Polycyclic presentation:
2^6,509|a^2=f,b^2=e,c^2=e,b^a=be,d^a=de,g^a=g^301,c^b=ce,g^f=g^5081304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 1617);