Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C7×C22⋊C4 ⋊ C22 |
| Hall | C3×C7 ⋊ #458 |
| Sylow | C7 ⋊ #5053 |
| Sylow | C3 ⋊ #89514 |
320 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^6,3,7|c^2=ef,c^a=ce,d^a=df,h^a=h^6,c^b=cd,e^b=ef,g^b=g^2,d^c=df93 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1801);