Finite Group DatabasebetaFinite Group Databasebeta| order | 2240 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | AGL(1,𝔽5)×(C2×D7)⋊C4 |
| Fitting | C2×C4×C5×C7 ⋊ C2×C4 |
| Hall | C5×C7 ⋊ C4×C22⋊C4 |
| Sylow | C7 ⋊ C22⋊C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×(C2×D7)⋊C4 |
516 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
170 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×(C2×AGL(1,𝔽7))⋊C4, D7×C22⋊C4×AGL(1,𝔽5), AGL(1,𝔽5)×#6445, … |
| maximal normal subgroup of | AGL(1,𝔽5)×(C2×AGL(1,𝔽7))⋊C4, D7×C22⋊C4×AGL(1,𝔽5), AGL(1,𝔽5)×#6445, … |
Past the SmallGroups library coverage — no SmallGroups id.