Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of A4×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×A4×D7 |
| Fitting | C22×C7×C8 ⋊ C2×C3 |
| derived | C22×C7 ⋊ C2×C3×C8 |
| Hall | C22×C8×D7 ⋊ C3 |
| Sylow | C7 ⋊ C2×C8×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | A4×D7 |
| commutator, hypocenter | C22×C7 | C2×C3×C8 |
| Frattini | C4 | C2×A4×D7 |
| Fitting | C22×C7×C8 | C2×C3 |
| socle | C23×C7 | C2×C3×C4 |
| prime radical | C2×A4×D7 | C4 |
| cosocle | C22×C4×C7 | C22×C3 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C8 | |
186 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6883);