Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×D11×H(3,𝔽3) |
| unambiguous semidirect product | C11⋊(C22×H(3,𝔽3)) |
| unambiguous semidirect product | (C2×C11)⋊(C2×H(3,𝔽3)) |
| unambiguous semidirect product | (C2×C32×D11)⋊C3 |
| Fitting | C2×C11×H(3,𝔽3) ⋊ C2 |
| Hall | C11×H(3,𝔽3) ⋊ C22 |
| Sylow | C11 ⋊ C22×H(3,𝔽3) |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 50);