Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | #89444⋊C3 |
| Fitting | C7×#95 ⋊ C2×C3 |
| Hall | #89444 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #394 |
| Sylow | C7 ⋊ C3×#394 |
476 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^3,3,2^3,7|b^2=g,c^2=fg,b^a=bg,c^a=cf,h^a=h^6,c^b=ce,h^d=h^286 conjugacy classes — view the full character table.
| maximal subgroup of | #72276654, AGL(1,𝔽7)×#394 |
| maximal normal subgroup of | #72276654, AGL(1,𝔽7)×#394 |
| maximal quotient of | #72276814 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 863);