Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C7 ⋊ #359 |
| Sylow | C7 ⋊ #4497 |
| Sylow | C3 ⋊ #89305 |
112 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^6,3,7|a^2=d,b^2=cdef,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,h^a=h^6,g^b=g^2180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 224);