Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of D3×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C3 |
| direct product | D3×C11×C3⋊D3 |
| unambiguous semidirect product | (C3×D3)⋊(D3×C11) |
| unambiguous semidirect product | (C3⋊(C3⋊D3))⋊(C2×C11) |
| Fitting, socle, Hall | C33×C11 ⋊ C22 |
| derived, Sylow | C33 ⋊ C22×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D3×C3⋊D3 |
| commutator, cosocle, hypocenter | C33 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C33×C11 | C22 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C11 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×D11, D3×C3⋊D3×C11⋊C5, D33×C11, … |
| maximal normal subgroup of | D3×C3⋊D3×D11, D3×C3⋊D3×C11⋊C5, D33×C11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 85);