Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C509 ⋊ C4 |
| Sylow | C509 ⋊ #440 |
120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4072 |
Polycyclic presentation:
2^6,509|a^2=e,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^208,d^b=df,g^c=g^301,g^e=g^508911 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 1588);