Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of D3×C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C13⋊C9 |
| unambiguous semidirect product | C3⋊(C4×C13⋊C9) |
| unambiguous semidirect product | (Dic3×C13)⋊C9 |
| derived | C3×C13 ⋊ C4×C9 |
| Hall | C3×C13⋊C9 ⋊ C4 |
| Sylow | C13 ⋊ C9×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D3×C13⋊C3 |
| commutator, hypocenter | C3×C13 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C32×C13 | C2×C3 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C2×C3 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 468 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 28);