Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of D3×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×D3×D11 |
| unambiguous semidirect product | (D3×C11)⋊(C2×C32) |
| unambiguous semidirect product | (C3×D11)⋊(C2×C32) |
| unambiguous semidirect product | D33⋊(C2×C32) |
| Fitting, socle, Hall | C33×C11 ⋊ C22 |
| derived | C3×C11 ⋊ C22×C32 |
| Sylow | C33 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×C32×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D3×D11 |
| commutator, cosocle, hypocenter | C3×C11 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C33×C11 | C22 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C32 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×D11, C32×D3×AGL(1,𝔽11), C3×D32×D11 |
| maximal normal subgroup of | D3×C3⋊D3×D11, C32×D3×AGL(1,𝔽11), C3×D32×D11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 79);