Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | AGL(1,𝔽5)×#454 |
| Fitting | C5×#454 ⋊ C4 |
| Sylow | C5 ⋊ C4×#454 |
1390 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3288, AGL(1,𝔽5)×#3021, #72221465, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3288, AGL(1,𝔽5)×#3021, #72221465, … |
| maximal quotient of | #72223492, #72226376 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1106460);