Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C2×#10618000 |
| Fitting | C22×C5×#125 ⋊ C2 |
| Sylow | C5 ⋊ C2×#3515 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C24×D5 |
| commutator, cosocle | C22×C5 | C26 |
| Frattini | C22 | C25×D5 |
| Fitting | C22×C5×#125 | C2 |
| socle | C23×C5 | C25 |
| hypercenter | C22×#125 | D5 |
| hypocenter | C5 | C2×#3515 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C22×#125 | |
7142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1077672);