Finite Group DatabasebetaFinite Group Databasebeta| order | 2560 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C210 |
| direct product | D5×#8541 |
| Fitting | C5×#8541 ⋊ C2 |
| Sylow | C5 ⋊ C2×#8541 |
23164 conjugacy classes of subgroups; only the 473 normal subgroups are shown.
This group has 23164 conjugacy classes of subgroups — too many to draw. Only its 473 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #72243209, AGL(1,𝔽5)×#8541, D5×#347042 |
| maximal normal subgroup of | #72243209, AGL(1,𝔽5)×#8541, D5×#347042 |
Past the SmallGroups library coverage — no SmallGroups id.