Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of AGL(1,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #261⋊C27 |
| derived, Sylow | C13 ⋊ C4×C27 |
| Hall | C13⋊C27 ⋊ C4 |
| Hall | #261 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | AGL(1,𝔽13) |
| commutator, hypocenter | C13 | C4×C27 |
| Fitting | C9×C13 | C3×C4 |
| socle | C3×C13 | C4×C9 |
| prime radical | C3×D13 | C2×C9 |
| cosocle | C9×D13 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 351 |
Polycyclic presentation:
2,3,2,3^2,13|a^2=c,b^3=d,d^3=e,f^a=f^8,f^b=f^9,f^c=f^12117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 7);