Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×C5×C7×C8 ⋊ C2 |
| Hall | C3×C5×C7 ⋊ M16 |
| Hall | C5×C7 ⋊ ΓL(1,𝔽25) |
| Hall | C3×C7 ⋊ #676 |
| Hall | C3×C5 ⋊ #1131 |
| Sylow | C7 ⋊ #6705 |
| Sylow | C5 ⋊ #66622 |
| Sylow | C3 ⋊ #10587893 |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 840 |
Polycyclic presentation:
2^4,3,5,7|b^2=c,c^2=d,b^a=bd,e^a=e^2,f^a=f^4,g^a=g^6426 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 374);