Finite Group DatabasebetaFinite Group Databasebeta| order | 2240 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D7×#4007 |
| Fitting | C5×C7×D4 ⋊ C2×C4 |
| Hall | C5×C7 ⋊ C2×#102 |
| Sylow | C7 ⋊ C2×#4007 |
| Sylow | C5 ⋊ D7×#102 |
404 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
95 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#4007, D7×D8×AGL(1,𝔽5), D7×#65731, … |
| maximal normal subgroup of | AGL(1,𝔽7)×#4007, D7×D8×AGL(1,𝔽5), D7×#65731, … |
Past the SmallGroups library coverage — no SmallGroups id.