Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of C22⋊(C13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C13⋊C27) |
| unambiguous semidirect product | C13⋊(C22⋊C27) |
| derived, Hall | C22×C13 ⋊ C27 |
| Sylow | C13 ⋊ C22⋊C27 |
| Sylow | C22 ⋊ C13⋊C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | C22⋊(C13⋊C3) |
| commutator, hypocenter | C22×C13 | C27 |
| Fitting, cosocle | C22×C9×C13 | C3 |
| socle, prime radical | C22×C3×C13 | C9 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C9 | |
22 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 702 |
Polycyclic presentation:
3^3,2^2,13|a^3=b,b^3=c,d^a=de,e^a=d,f^a=f^3180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 14);