Finite Group DatabasebetaFinite Group Databasebeta| order | 726 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C112 · Schur multiplier (H2) = C11 |
| direct product | D3×C112 |
| unambiguous semidirect product | C3⋊(C2×C112) |
| Fitting, socle, Hall | C3×C112 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | D3 |
| commutator, cosocle, hypocenter | C3 | C2×C112 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C112 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 363 |
363 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C11×D11, D3×C11⋊D11, C2×D3×C112, … |
| maximal normal subgroup of | D3×C11×D11, D3×C11⋊D11, C2×D3×C112, … |
| maximal quotient of | C112×Dic3, C2×D3×C112, C112×D9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(726, 10);