Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#10620529 |
| Hall | C3×C7 ⋊ C2×#95 |
| Sylow | C7 ⋊ C2×C3⋊#95 |
| Sylow | C3 ⋊ C2×C7⋊#95 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D3×D7 |
| commutator | C2×C3×C7 | C2×C42 |
| Frattini | C23 | C2×D3×D7 |
| Fitting, socle, prime radical | C24×C3×C7 | C22 |
| cosocle | C23×C3×C7 | C23 |
| hypocenter | C3×C7 | C2×#95 |
| LCS | G ▷ C2×C3×C7 ▷ C3×C7 | |
| UCS | C1 ◁ C24 | |
660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1344 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4137);