Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | Dic3×(C2×D7)⋊C4 |
| Hall | C3×C7 ⋊ C4×C22⋊C4 |
| Sylow | C7 ⋊ Dic3×C22⋊C4 |
| Sylow | C3 ⋊ C4×(C2×D7)⋊C4 |
516 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 3538);