Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C213 |
| direct product | C22×#65536 |
| Sylow | C5 ⋊ C22×#379 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C22×D5 |
| commutator | C22×C5 | C24×C4 |
| Frattini | C23 | C24×D5 |
| Fitting, prime radical | C27×C5 | C2 |
| socle | C25×C5 | C23 |
| cosocle | C23×C5 | C25 |
| hypercenter | C27 | D5 |
| hypocenter | C5 | C22×#379 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C25 ◁ C27 | |
33214 conjugacy classes of subgroups; only the 3307 normal subgroups are shown.
This group has 33214 conjugacy classes of subgroups — too many to draw. Only its 3307 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 327823);