Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C127 ⋊ #1584 |
152 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,127|a^2=e,b^2=f,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^126,d^b=df,h^b=h^126,h^c=h^1261802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 3363);