Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D3×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | C4×Dic3×Dic7 |
| derived, Hall | C3×C7 ⋊ C43 |
| Sylow | C7 ⋊ C42×Dic3 |
| Sylow | C3 ⋊ C42×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D3×D7 |
| commutator, hypocenter | C3×C7 | C43 |
| Frattini | C23 | C2×D3×D7 |
| Fitting | C22×C3×C4×C7 | C22 |
| socle, prime radical, cosocle | C23×C3×C7 | C23 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C22×C4 | |
516 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1344 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 3166);