Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#10587902 |
| Fitting | C2×C3×C4×C5×C7 ⋊ C2 |
| Hall | C3×C5×C7 ⋊ C22⋊C4 |
| Hall | C5×C7 ⋊ C3×C22⋊C4 |
| Hall | C3×C7 ⋊ #685 |
| Hall | C3×C5 ⋊ (C2×D7)⋊C4 |
| Sylow | C7 ⋊ C3×#685 |
| Sylow | C5 ⋊ C3×(C2×D7)⋊C4 |
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 840 |
438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 319);