Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C4 |
| direct product | C4×C5×Dic21 |
| derived, Hall | C3×C7 ⋊ C42×C5 |
| Hall | C3×C5×C7 ⋊ C42 |
| Hall | C5×C7 ⋊ C4×Dic3 |
| Hall | C3×C5 ⋊ C4×Dic7 |
| Sylow | C7 ⋊ C4×C5×Dic3 |
| Sylow | C3 ⋊ C4×C5×Dic7 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1680 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 348);