Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×D4×C4⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(D4×C4⋊C4) |
| Fitting | C2×C4×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ C2×D4×C4⋊C4 |
4718 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D42×AGL(1,𝔽5) |
| maximal normal subgroup of | C2×D42×AGL(1,𝔽5) |
| maximal quotient of | #72221485 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114221);