Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of C3⋊(C3⋊#261) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C3⋊(C3⋊#261) |
| unambiguous semidirect product | C3⋊(C3×C3⋊#261) |
| Fitting, socle, Hall | C33×C13 ⋊ C4 |
| derived | C32×C13 ⋊ C3×C4 |
| Sylow | C33 ⋊ #261 |
| Sylow | C13 ⋊ C3×C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C3⋊#261) |
| commutator, hypocenter | C32×C13 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C33×C13 | C4 |
| prime radical | C33×D13 | C2 |
| cosocle | C32×D13 | C2×C3 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C3 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 234 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C3⋊D3×#261, D3×C3⋊(C3⋊#261), #72276952, … |
| maximal normal subgroup of | C3×C3⋊D3×#261, D3×C3⋊(C3⋊#261), #72276952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 197);