Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of AGL(1,𝔽27) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C3⋊(C3⋊Dic3))⋊C13 |
| unambiguous semidirect product | (C33⋊C13)⋊C4 |
| derived, Sylow | C33 ⋊ C4×C13 |
| Hall | C33⋊C13 ⋊ C4 |
| Hall | C3⋊(C3⋊Dic3) ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽27) |
| commutator, hypocenter | C33 | C4×C13 |
| Fitting, socle, cosocle | C2×C33 | C2×C13 |
| prime radical | C2×C33⋊C13 | C2 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,13,2,3^3|a^2=c,d^a=d^2,e^a=e^2,f^a=f^2,d^b=f,e^b=d^2f,f^b=d^2e^2f54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 160);