Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #89517⋊C3 |
| Fitting | C7×#100 ⋊ C2×C3 |
| Hall | #89517 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #413 |
| Sylow | C7 ⋊ C3×#413 |
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^3,3,2^3,7|c^2=e,e^2=g,b^a=bg,h^a=h^6,c^b=cf,e^b=eg,f^c=fg,h^d=h^277 conjugacy classes — view the full character table.
| maximal subgroup of | #72259820, #72259838, #72259859, … |
| maximal normal subgroup of | #72259820, #72259838, #72259859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 934);