Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#16860811 |
| Fitting | Q82×C251 ⋊ C2 |
| Sylow | C251 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D251 |
| commutator, socle, cosocle | C22×C251 | C25 |
| Fitting | Q82×C251 | C2 |
| prime radical | C2×#16860811 | C22 |
| hypercenter | Q82 | D251 |
| hypocenter | C251 | Q8×#41 |
| LCS | G ▷ C22×C251 ▷ C251 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
1068 conjugacy classes of subgroups; only the 529 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 529 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 16064 |
3175 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 18093);