Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #89261⋊C3 |
| Hall | #89261 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #347 |
| Sylow | C7 ⋊ C3×#347 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^2,3,2^4,7|a^2=e,b^2=d,e^2=f,f^2=g,b^a=bf,d^a=dg,h^a=h^6,e^b=eg,h^c=h^286 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#347, #72228671, #72228676 |
| maximal normal subgroup of | AGL(1,𝔽7)×#347, #72228671, #72228676 |
| maximal quotient of | #72276555 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 25);