Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #336×C131 ⋊ C2 |
| Sylow | C131 ⋊ #1866 |
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4192 |
Polycyclic presentation:
2^7,131|a^2=f,b^2=f,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^130,d^b=dg,e^b=eg,h^b=h^130,d^c=dg,e^c=eg,h^c=h^1302638 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 4788);