Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C22⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C22×C4×C22⋊ΓL(1,𝔽8) |
| Fitting, Hall | C24×C4×C7 ⋊ C3 |
| derived | C22×C7 ⋊ C22×C3×C4 |
| Sylow | C24×C4 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C22×C4×A4 |
634 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11598);