Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #417×C131 ⋊ C2 |
| Sylow | C131 ⋊ #3012 |
764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 149 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|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^130,e^b=eg,d^c=dg,h^c=h^1301462 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 13816);