Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| unambiguous semidirect product | #10587739⋊M32 |
| Sylow | C137 ⋊ C4×M32 |
196 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2192 |
Polycyclic presentation:
2^7,137|a^2=d,b^2=e,d^2=f,f^2=g,c^a=cg,h^a=h^127,h^b=h^37,h^d=h^100,h^e=h^136,h^f=h^136352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21670);