Finite Group DatabasebetaFinite Group Databasebeta| order | 2240 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×C7⋊AGL(1,𝔽5) |
| Fitting | C5×C7×M16 ⋊ C4 |
| Hall | C5×C7 ⋊ C4×M16 |
| Sylow | C7 ⋊ M16×AGL(1,𝔽5) |
| Sylow | C5 ⋊ M16×Dic7 |
284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 109 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 | M16×ΓL(1,𝔽8)⋊AGL(1,𝔽5), D7×M16×AGL(1,𝔽5), AGL(1,ℤ/8)×C7⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | M16×ΓL(1,𝔽8)⋊AGL(1,𝔽5), D7×M16×AGL(1,𝔽5), AGL(1,ℤ/8)×C7⋊AGL(1,𝔽5), … |
Past the SmallGroups library coverage — no SmallGroups id.