Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×Q8×C22⋊ΓL(1,𝔽8) |
| Fitting, Hall | C23×C7×Q8 ⋊ C3 |
| Sylow | C23×Q8 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C2×Q8×A4 |
410 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11600);