Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of C22⋊(C13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C22⋊(C13⋊C9) |
| unambiguous semidirect product | (C22×C3)⋊(C13⋊C9) |
| unambiguous semidirect product | (C3×C13)⋊(C22⋊C9) |
| derived, Hall | C22×C13 ⋊ C3×C9 |
| Sylow | C13 ⋊ C3×C22⋊C9 |
| Sylow | C22 ⋊ C3×C13⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C22⋊(C13⋊C3) |
| commutator, hypocenter | C22×C13 | C3×C9 |
| Frattini | C3 | C3×C22⋊(C13⋊C3) |
| Fitting, socle, prime radical | C22×C32×C13 | C3 |
| cosocle | C22×C3×C13 | C32 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C32 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 702 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 139);