Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C2×C7×#805 |
| Fitting | C2×C3×C42×C7 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×#104 |
| Sylow | C3 ⋊ C2×C7×#104 |
340 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5261);