Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of D3×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | D3×C11×D9 |
| unambiguous semidirect product | (C3×D9)⋊(C2×C11) |
| unambiguous semidirect product | (D3×C9)⋊(C2×C11) |
| unambiguous semidirect product | (C3⋊D9)⋊(C2×C11) |
| Fitting, Hall | C3×C9×C11 ⋊ C22 |
| derived, Sylow | C3×C9 ⋊ C22×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D3×D9 |
| commutator, cosocle, hypocenter | C3×C9 | C22×C11 |
| Frattini | C3 | D32×C11 |
| Fitting | C3×C9×C11 | C22 |
| socle | C32×C11 | C2×D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C11 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 198 |
198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 37);