Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C7×Q32 ⋊ C2 |
| Hall | C3×C7 ⋊ #510 |
| Sylow | C7 ⋊ #4918 |
| Sylow | C3 ⋊ #89690 |
164 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 47 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|b^2=f,c^2=f,d^2=ef,e^2=f,c^a=cf,g^a=g^2,h^a=h^6,c^b=cd,d^b=de,e^b=ef,d^c=de,e^c=ef126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5844);