Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | Dic7×ΓL(1,𝔽25) |
| Hall | C3×C7 ⋊ C4×M16 |
| Sylow | C7 ⋊ C4×ΓL(1,𝔽25) |
| Sylow | C3 ⋊ M16×Dic7 |
284 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 2247);