Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#10621364 |
| Fitting | C2×C3×C7×C22⋊C4 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×C4×D4 |
| Sylow | C7 ⋊ C2×#67⋊C4 |
| Sylow | C3 ⋊ C2×(C22⋊D7)⋊C4 |
852 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10865);