Finite Group DatabasebetaFinite Group Databasebeta| order | 2240 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#65767 |
| Fitting | C2×C5×C7×D4 ⋊ C4 |
| Hall | C5×C7 ⋊ #418 |
| Sylow | C5 ⋊ C7×#418 |
380 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
224 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#65767, C7×AGL(1,𝔽5)×AGL(1,ℤ/8), #72218596, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×#65767, C7×AGL(1,𝔽5)×AGL(1,ℤ/8), #72218596, … |
Past the SmallGroups library coverage — no SmallGroups id.