Finite Group DatabasebetaFinite Group Databasebeta| order | 5120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | AGL(1,𝔽5)×#7389 |
| Fitting | C5×#7389 ⋊ C4 |
| Sylow | C5 ⋊ C4×#7389 |
1132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×AGL(1,ℤ/32) |
| maximal normal subgroup of | AGL(1,𝔽5)×AGL(1,ℤ/32) |
Past the SmallGroups library coverage — no SmallGroups id.