Finite Group DatabasebetaFinite Group Databasebeta| order | 3920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×(C2×D7)⋊AGL(1,𝔽5) |
| Hall | C5×C72 ⋊ C22⋊C4 |
| Sylow | C72 ⋊ C22⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C7×(C2×D7)⋊C4 |
184 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 140 |
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72243483, C7×AGL(1,𝔽5)×C22⋊D7, #72243508, … |
| maximal normal subgroup of | #72243483, C7×AGL(1,𝔽5)×C22⋊D7, #72243508, … |
Past the SmallGroups library coverage — no SmallGroups id.