Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×H(5,𝔽2)×C251 ⋊ C2 |
| Sylow | C251 ⋊ #3026 |
800 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 161 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|b^a=be,c^a=cf,d^a=dg,h^a=h^250,f^b=fg,e^c=eg4279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 13907);