Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×(C22⋊D7)⋊C3 |
| unambiguous semidirect product | (C8×C22⋊D7)⋊C3 |
| Fitting | C22×C7×C8 ⋊ C2×C3 |
| Hall | C8×C22⋊D7 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C8×D4 |
| Sylow | C7 ⋊ C3×C8×D4 |
268 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1297);