Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5×C7 ⋊ M16 |
| Hall | C5×C7 ⋊ #208 |
| Hall | C3×C7 ⋊ #704 |
| Hall | C3×C5 ⋊ #1136 |
| Sylow | C7 ⋊ #6762 |
| Sylow | C5 ⋊ #66627 |
| Sylow | C3 ⋊ #10587935 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 840 |
Polycyclic presentation:
2^4,3,5,7|a^2=c,c^2=d,b^a=bd,e^a=e^2,f^a=f^2,g^a=g^6,f^c=f^4174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 649);