Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | #90213⋊C3 |
| Fitting | C7×#117 ⋊ C2×C3 |
| Hall | #90213 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C4×#41 |
| Sylow | C7 ⋊ C3×C4×#41 |
620 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^4,3,2^2,7|b^2=g,d^2=f,c^a=cg,h^a=h^6,d^c=dg,h^e=h^2140 conjugacy classes — view the full character table.
| maximal subgroup of | #72218414, #72218555, #72218598, … |
| maximal normal subgroup of | #72218555, #72218598, C4×#41×AGL(1,𝔽7), … |
| maximal quotient of | #72218414 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6548);