Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #89297⋊C3 |
| Hall | #89297 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #346 |
| Sylow | C7 ⋊ C3×#346 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^2,3,2^4,7|a^2=e,b^2=d,d^2=f,f^2=g,b^a=bg,h^a=h^6,h^c=h^2152 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#346, #72276641, #72276642, … |
| maximal normal subgroup of | AGL(1,𝔽7)×#346, #72276641, #72276642, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 63);