Finite Group DatabasebetaFinite Group Databasebeta| order | 2560 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | D5×#12705 |
| Fitting | C5×#12705 ⋊ C2 |
| Sylow | C5 ⋊ C2×#12705 |
8380 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#12705, #72243033, D5×#511790 |
| maximal normal subgroup of | AGL(1,𝔽5)×#12705, #72243033, D5×#511790 |
Past the SmallGroups library coverage — no SmallGroups id.