Finite Group DatabasebetaFinite Group Databasebeta| order | 2240 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×D8×AGL(1,𝔽5) |
| Fitting | C5×C7×D8 ⋊ C4 |
| Hall | C5×C7 ⋊ C4×D8 |
| Sylow | C5 ⋊ C4×C7×D8 |
268 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
245 conjugacy classes — view the full character table.
| maximal subgroup of | D8×AGL(1,𝔽5)×ΓL(1,𝔽8), D7×D8×AGL(1,𝔽5), C7×AGL(1,𝔽5)×AGL(1,ℤ/8), … |
| maximal normal subgroup of | D8×AGL(1,𝔽5)×ΓL(1,𝔽8), D7×D8×AGL(1,𝔽5), C7×AGL(1,𝔽5)×AGL(1,ℤ/8), … |
Past the SmallGroups library coverage — no SmallGroups id.