Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of (C3⋊D3)⋊(C13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C3⋊Dic3)⋊(C13⋊C3) |
| derived | C32×C13 ⋊ C3×C4 |
| Hall | C32⋊(C13⋊C3) ⋊ C4 |
| Sylow | C13 ⋊ (C3⋊Dic3)⋊C3 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 468 |
Polycyclic presentation:
2,3,2,3^2,13|a^2=c,d^a=d^2,e^a=e^2,d^b=de,f^b=f^368 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 29);