Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D3×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C3⋊C8×C7⋊C8 |
| derived, Hall | C3×C7 ⋊ C82 |
| Sylow | C7 ⋊ C8×C3⋊C8 |
| Sylow | C3 ⋊ C8×C7⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C42 | D3×D7 |
| commutator, hypocenter | C3×C7 | C82 |
| Fitting, cosocle | C3×C42×C7 | C22 |
| socle, prime radical | C22×C3×C7 | C42 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C42 | |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1344 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 147);