Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C9×C11 |
| unambiguous semidirect product | C3⋊(C22×C9×C11) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C9×C11) |
| Fitting | C2×C3×C9×C11 ⋊ C2 |
| derived | C3 ⋊ C22×C9×C11 |
| Hall | C3×C9×C11 ⋊ C22 |
| Sylow | C3×C9 ⋊ C22×C11 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 396 |
594 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×D3×C9×C11 |
| maximal normal subgroup of | C22×D3×C9×C11 |
| maximal quotient of | C22×D3×C9×C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 53);