Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C7×#41 ⋊ C22 |
| Hall | C3×C7 ⋊ C2×AGL(1,ℤ/8) |
| Sylow | C7 ⋊ D3×AGL(1,ℤ/8) |
| Sylow | C3 ⋊ D7×AGL(1,ℤ/8) |
596 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^6,3,7|e^2=f,d^a=de,e^a=ef,h^a=h^6,d^b=de,e^b=ef,g^b=g^2,d^c=df,e^d=ef96 conjugacy classes — view the full character table.
| maximal subgroup of | #72244303, D3×D7×AGL(1,ℤ/8), #72244353, … |
| maximal normal subgroup of | #72244303, D3×D7×AGL(1,ℤ/8), #72244353, … |
| maximal quotient of | #72245955 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 9844);