Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×Q8×#67 |
| Fitting | C22×C3×C7×Q8 ⋊ C2 |
| Hall | C3×C7 ⋊ D4×Q8 |
| Sylow | C3 ⋊ C7×D4×Q8 |
560 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10820);