Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×M16×C137 ⋊ C4 |
| Sylow | C137 ⋊ C2×H(3,ℤ/4) |
404 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 128 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=e,b^2=f,d^2=g,b^a=bd,f^a=fg,h^a=h^37,e^b=eg,h^b=h^100,h^c=h^136,h^e=h^136,h^f=h^136724 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 20182);