Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C137 ⋊ #1998 |
228 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8768 |
Polycyclic presentation:
2^7,137|a^2=f,b^2=def,c^2=eg,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^37,d^b=dg,f^b=fg,h^b=h^100,h^f=h^136712 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 20704);