Finite Group DatabasebetaFinite Group Databasebeta| order | 726 |
| isoclinism | isoclinic class of D121 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D121 |
| unambiguous semidirect product | C121⋊(C2×C3) |
| Fitting, Hall | C3×C121 ⋊ C2 |
| derived, Sylow | C121 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D121 |
| commutator, cosocle, hypocenter | C121 | C2×C3 |
| Frattini | C11 | C3×D11 |
| Fitting | C3×C121 | C2 |
| socle | C3×C11 | D11 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 363 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D121, C2×C3×D121, C9×D121, … |
| maximal normal subgroup of | D3×D121, C2×C3×D121, C9×D121, … |
| maximal quotient of | C3×Dic121, C2×C3×D121, C9×D121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(726, 2);