Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #89300⋊C3 |
| Hall | #89300 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #367 |
| Sylow | C7 ⋊ C3×#367 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^2,3,2^4,7|a^2=e,b^2=dfg,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^6,h^c=h^298 conjugacy classes — view the full character table.
| maximal subgroup of | #72276618, #72276641, AGL(1,𝔽7)×#367 |
| maximal normal subgroup of | #72276618, #72276641, AGL(1,𝔽7)×#367 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 64);