Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×D7×D20 |
| Fitting | C3×C4×C5×C7 ⋊ C22 |
| Hall | C3×C5×C7 ⋊ C2×D4 |
| Hall | C5×C7 ⋊ C2×C3×D4 |
| Hall | C3×C7 ⋊ C2×D20 |
| Hall | C3×C5 ⋊ D4×D7 |
| Sylow | C7 ⋊ C2×C3×D20 |
| Sylow | C5 ⋊ C3×D4×D7 |
216 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 420 |
195 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 662);