Finite Group DatabasebetaFinite Group Databasebeta| order | 2240 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×C22⋊C4×AGL(1,𝔽5) |
| Fitting | C5×C7×C22⋊C4 ⋊ C4 |
| Hall | C5×C7 ⋊ C4×C22⋊C4 |
| Sylow | C5 ⋊ C4×C7×C22⋊C4 |
516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×AGL(1,𝔽5)×ΓL(1,𝔽8), D7×C22⋊C4×AGL(1,𝔽5), C7×AGL(1,𝔽5)×#120, … |
| maximal normal subgroup of | C22⋊C4×AGL(1,𝔽5)×ΓL(1,𝔽8), D7×C22⋊C4×AGL(1,𝔽5), C7×AGL(1,𝔽5)×#120, … |
Past the SmallGroups library coverage — no SmallGroups id.