Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C212 |
| direct product | C23×(C2×AGL(1,𝔽5))⋊C4 |
| unambiguous semidirect product | D5⋊(C22×#95) |
| Fitting | C24×C4×C5 ⋊ C4 |
| Sylow | C5 ⋊ C23×#95 |
14334 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114090);