Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | Dic13⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×Dic13⋊C3)⋊C3 |
| Hall | C32⋊(C13⋊C3) ⋊ C4 |
| Hall | Dic13 ⋊ H(3,𝔽3) |
| Sylow | C13 ⋊ C4×H(3,𝔽3) |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 468 |
Polycyclic presentation:
2,3^2,2,3,13|a^2=d,f^a=f^12,c^b=ce,f^b=f^380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 24);