Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of C3⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×C3⋊#261 |
| unambiguous semidirect product | C3⋊(C32×#261) |
| Fitting, socle, Hall | C33×C13 ⋊ C4 |
| derived | C3×C13 ⋊ C32×C4 |
| Sylow | C33 ⋊ #261 |
| Sylow | C13 ⋊ C32×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊#261 |
| commutator, hypocenter | C3×C13 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C33×C13 | C4 |
| prime radical | C33×D13 | C2 |
| cosocle | C3×D13 | C2×C32 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C32 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 234 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×C3⋊#261, C32×D3×#261, #72276952, … |
| maximal normal subgroup of | C3⋊D3×C3⋊#261, C32×D3×#261, #72276952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 196);