Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C7 · Schur multiplier (H2) = C43 |
| direct product | C42×C7×Dic3 |
| unambiguous semidirect product | C3⋊(C43×C7) |
| derived, Sylow | C3 ⋊ C43×C7 |
| Hall | C3×C7 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42×C7 | D3 |
| commutator, hypocenter | C3 | C43×C7 |
| Frattini | C23 | C22×D3×C7 |
| Fitting | C2×C3×C42×C7 | C2 |
| socle, prime radical | C23×C3×C7 | C23 |
| cosocle | C23×C3 | C23×C7 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C42×C7 | |
516 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1344 |
672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5252);