Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×D3×Q8×D7 |
| Fitting | C2×C3×C7×Q8 ⋊ C22 |
| Hall | C3×C7 ⋊ C23×Q8 |
| Sylow | C7 ⋊ C22×D3×Q8 |
| Sylow | C3 ⋊ C22×Q8×D7 |
1700 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11543);