Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5×C7 ⋊ SD16 |
| Hall | C5×C7 ⋊ #204 |
| Hall | C3×C7 ⋊ #677 |
| Hall | C3×C5 ⋊ #1143 |
| Sylow | C7 ⋊ #6706 |
| Sylow | C5 ⋊ #66568 |
| Sylow | C3 ⋊ #10587849 |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 840 |
Polycyclic presentation:
2^4,3,5,7|a^2=c,b^2=d,c^2=d,b^a=bcd,g^a=g^6,c^b=cd,e^b=e^2,f^b=f^4162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 156);