Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5×C7 ⋊ C22⋊C4 |
| Hall | C5×C7 ⋊ (C2×D3)⋊C4 |
| Hall | C3×C7 ⋊ #685 |
| Hall | C3×C5 ⋊ (C2×D7)⋊C4 |
| Sylow | C7 ⋊ #6667 |
| Sylow | C5 ⋊ #66575 |
| Sylow | C3 ⋊ #10587902 |
136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 840 |
Polycyclic presentation:
2^4,3,5,7|a^2=d,b^2=cd,b^a=bc,f^a=f^4,g^a=g^6,e^b=e^2222 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 238);