Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| isoclinism | isoclinic class of D3×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×Dic3×D7 |
| derived, Hall | C3×C7 ⋊ C22×C4×C5 |
| Hall | C3×C5×C7 ⋊ C22×C4 |
| Hall | C5×C7 ⋊ C22×Dic3 |
| Hall | C3×C5 ⋊ C2×C4×D7 |
| Sylow | C7 ⋊ C22×C5×Dic3 |
| Sylow | C3 ⋊ C2×C4×C5×D7 |
216 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 840 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 692);