Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C3×D4×D28 |
| Fitting | C3×C4×C7×D4 ⋊ C2 |
| Hall | C3×C7 ⋊ D42 |
| Sylow | C7 ⋊ C3×D42 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3 | C23×D7 |
| commutator, cosocle | C22×C7 | C24×C3 |
| Frattini | C22 | C23×C3×D7 |
| Fitting | C3×C4×C7×D4 | C2 |
| socle | C22×C3×C7 | C24 |
| hypercenter | C3×C4×D4 | D7 |
| hypocenter | C7 | C3×D42 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22×C3 ◁ C3×C4×D4 | |
856 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10183);