Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C137 ⋊ #1378 |
132 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4384 |
Polycyclic presentation:
2^7,137|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,e^a=eg,h^a=h^127,c^b=cg,h^d=h^100,h^f=h^136214 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21588);