Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×2−1+4⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C2×2−1+4)⋊ΓL(1,𝔽8) |
| Fitting, Hall | C2×C7×2−1+4 ⋊ C3 |
| Sylow | C2×2−1+4 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C2×2−1+4⋊C3 |
408 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11605);