Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C137 ⋊ C8 |
| Sylow | C137 ⋊ #1565 |
180 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1096 |
Polycyclic presentation:
2^7,137|a^2=e,b^2=d,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^127,c^b=cf,h^e=h^100,h^g=h^136214 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21635);