Finite Group DatabasebetaFinite Group Databasebeta| order | 2560 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D5×#7389 |
| Fitting | C5×#7389 ⋊ C2 |
| Sylow | C5 ⋊ C2×#7389 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#7389, D5×AGL(1,ℤ/32), #72242290 |
| maximal normal subgroup of | AGL(1,𝔽5)×#7389, D5×AGL(1,ℤ/32), #72242290 |
Past the SmallGroups library coverage — no SmallGroups id.