Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #120×C137 ⋊ C4 |
| Sylow | C137 ⋊ #1889 |
578 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 68 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=f,b^2=df,b^a=bd,c^a=ce,e^a=eg,h^a=h^37,e^b=eg,h^b=h^100,d^c=dg,f^c=fg,h^f=h^136508 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 20519);