Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#22548760 |
| Fitting | C23×D4×C251 ⋊ C2 |
| Sylow | C251 ⋊ C22×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D251 |
| commutator, cosocle | C2×C251 | C26 |
| Frattini | C2 | C25×D251 |
| Fitting | C23×D4×C251 | C2 |
| socle | C23×C251 | C24 |
| hypercenter | C23×D4 | D251 |
| hypocenter | C251 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
6560 conjugacy classes of subgroups; only the 3221 normal subgroups are shown.
This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8032 |
5068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 19311);