Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#103×C127 ⋊ C2 |
| Sylow | C127 ⋊ #3046 |
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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=g,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^126,d^b=dg,h^b=h^126,f^c=fg,h^c=h^1261796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 14065);