Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of D3×C3⋊D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | D3×C3⋊D33 |
| unambiguous semidirect product | (C3×D3)⋊D33 |
| unambiguous semidirect product | (D3×C11)⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C33×C11 ⋊ C22 |
| Sylow | C33 ⋊ C2×D11 |
| Sylow | C11 ⋊ D3×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C33×C11 | C22 |
| LCS | G ▷ C33×C11 | |
| UCS | C1 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×D11, D3×C3⋊(C3⋊AGL(1,𝔽11)), D32×D33 |
| maximal normal subgroup of | D3×C3⋊D3×D11, D3×C3⋊(C3⋊AGL(1,𝔽11)), D32×D33 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 86);