Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Fitting | C42×C137 ⋊ C8 |
| Sylow | C137 ⋊ #1274 |
168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 51 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,c^2=f,d^2=g,b^a=bc,e^a=ef,h^a=h^127,d^b=df,h^d=h^100,h^g=h^136316 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21513);