Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D3×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D21⋊C32 |
| derived, Hall | C3×C7 ⋊ C2×C32 |
| Sylow | C7 ⋊ D3×C32 |
| Sylow | C3 ⋊ D7×C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D3×D7 |
| commutator, hypocenter | C3×C7 | C2×C32 |
| Fitting, cosocle | C3×C7×C16 | C22 |
| socle | C2×C3×C7 | C2×C16 |
| prime radical | C2×D21 | C16 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C16 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^6,3,7|a^2=c,b^2=c,c^2=d,d^2=e,e^2=f,h^a=h^6,g^b=g^2240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 131);