Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
| unambiguous semidirect product | D137⋊#353 |
| Fitting | #127×C137 ⋊ C4 |
| Sylow | C137 ⋊ C2×#353 |
368 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 54 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,d^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^100,d^b=dg,e^b=efg,h^c=h^136,e^d=eg,h^e=h^136502 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 20776);