Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×H(5,𝔽2)×D251 |
| Fitting | C2×H(5,𝔽2)×C251 ⋊ C2 |
| Sylow | C251 ⋊ C22×H(5,𝔽2) |
6560 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.
This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4016 |
4318 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 19310);