Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #89285⋊C3 |
| Hall | #89285 ⋊ 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=d,e^2=fg,f^2=g,b^a=beg,h^a=h^6,e^b=ef,f^b=fg,h^c=h^280 conjugacy classes — view the full character table.
| maximal subgroup of | #72276619, #72276642, AGL(1,𝔽7)×#367 |
| maximal normal subgroup of | #72276619, #72276642, AGL(1,𝔽7)×#367 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 51);