Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C3⋊AGL(1,𝔽13) |
| unambiguous semidirect product | C3⋊(C3×AGL(1,𝔽13)) |
| unambiguous semidirect product | (C3⋊#261)⋊C32 |
| unambiguous semidirect product | (C3×C3⋊#261)⋊C3 |
| Fitting, socle | C32×C13 ⋊ C3×C4 |
| derived | C3×C13 ⋊ C32×C4 |
| Hall | C32×C13⋊C3 ⋊ C4 |
| Sylow | C13 ⋊ C32×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊AGL(1,𝔽13) |
| commutator, hypocenter | C3×C13 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13 | C3×C4 |
| prime radical | C32×D13⋊C3 | C2 |
| cosocle | C3×D13 | C2×C32 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C3 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 78 |
63 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 179);