Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
| direct product | Q8×#3963 |
| Sylow | C5 ⋊ Q8×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D5 |
| commutator | C22×C5 | C22×C42 |
| Fitting | C22×C4×C5×Q8 | C2 |
| socle, prime radical, cosocle | C24×C5 | C24 |
| hypercenter | C22×C4×Q8 | D5 |
| hypocenter | C5 | Q8×#95 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C22×C4×Q8 | |
2434 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1280 |
260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 91054);