Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C4 |
| direct product | C7×C42⋊C9 |
| unambiguous semidirect product | C42⋊(C7×C9) |
| derived, Sylow | C42 ⋊ C7×C9 |
| Hall | C42×C7 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C42⋊C3 |
| commutator, hypocenter | C42 | C7×C9 |
| Frattini | C22×C3 | C7×A4 |
| Fitting | C3×C42×C7 | C3 |
| socle, prime radical | C22×C3×C7 | A4 |
| cosocle | C3×C42 | C3×C7 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C3×C7 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 56);