Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #324×C137 ⋊ C2 |
| Sylow | C137 ⋊ #1459 |
332 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 81 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=e,c^2=g,e^2=g,b^a=bd,d^a=df,e^b=ef,h^b=h^136,h^c=h^1361540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 2827);