Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #322×C131 ⋊ C2 |
| Sylow | C131 ⋊ #1594 |
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8384 |
Polycyclic presentation:
2^7,131|a^2=e,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^130,c^b=cg,d^b=df,h^b=h^1302632 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 3425);