Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#10587906 |
| Hall | C3×C5×C7 ⋊ Q16 |
| Hall | C5×C7 ⋊ C3×Q16 |
| Hall | C3×C7 ⋊ #689 |
| Hall | C3×C5 ⋊ #1144 |
| Sylow | C7 ⋊ C3×#689 |
| Sylow | C5 ⋊ C3×#1144 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1680 |
276 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 323);