Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C3×C4 |
| direct product | C3×C7×C42⋊C3 |
| unambiguous semidirect product | C42⋊(C32×C7) |
| unambiguous semidirect product | (C3×C42)⋊(C3×C7) |
| Fitting | C3×C42×C7 ⋊ C3 |
| derived, Sylow | C42 ⋊ C32×C7 |
| Hall | C42×C7 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C42⋊C3 |
| commutator, cosocle, hypocenter | C42 | C32×C7 |
| Frattini | C22 | C3×C7×A4 |
| Fitting | C3×C42×C7 | C3 |
| socle | C22×C3×C7 | A4 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C3×C7 | |
52 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, 408);