Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C221 |
| direct product | C25×C4×D5 |
| Fitting | C25×C4×C5 ⋊ C2 |
| derived, Sylow | C5 ⋊ C26×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25×C4 | D5 |
| commutator, hypocenter | C5 | C26×C4 |
| Frattini | C2 | C26×D5 |
| Fitting | C25×C4×C5 | C2 |
| socle | C26×C5 | C22 |
| prime radical | C26×D5 | C2 |
| cosocle | C2×C5 | C27 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C25×C4 | |
111198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
512 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1083442);