Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C7 ⋊ #453 |
| Sylow | C7 ⋊ #5198 |
| Sylow | C3 ⋊ #90013 |
336 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^6,3,7|d^2=f,e^2=f,b^a=be,c^a=cd,d^a=df,e^a=ef,h^a=h^6,e^b=ef,g^b=g^2,d^c=df108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#90013, D7×#5198, #72244353, … |
| maximal normal subgroup of | D3×#90013, D7×#5198, #72244353, … |
| maximal quotient of | #72246895 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4123);