Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×3−1+2⋊C4 |
| unambiguous semidirect product | 3−1+2⋊(C4×C11) |
| unambiguous semidirect product | Dic9⋊(C3×C11) |
| unambiguous semidirect product | (C11×Dic9)⋊C3 |
| derived | C9 ⋊ C3×C4×C11 |
| Hall | C11×3−1+2 ⋊ C4 |
| Sylow | 3−1+2 ⋊ C4×C11 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 396 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17,20,15,16,19)(14,18)(21,22,23,24);(12,20,15,18,16,17,14,13,19)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 17);