Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C22⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×C8×C22⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C2×C7×C8)⋊A4 |
| Fitting, Hall | C23×C7×C8 ⋊ C3 |
| derived | C22×C7 ⋊ C2×C3×C8 |
| Sylow | C23×C8 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C2×C8×A4 |
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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, 10076);