Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | B(4,𝔽2)×C251 ⋊ C2 |
| Sylow | C251 ⋊ #3027 |
772 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 772 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.
| transitive degree | μt(G) = 4016 |
Polycyclic presentation:
2^7,251|d^2=g,b^a=be,c^a=cf,d^a=dg,f^b=fg,e^c=eg,h^d=h^2502029 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 13910);