Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#1094 |
| Hall | C22×C11 ⋊ 3−1+2 |
| Sylow | C22 ⋊ C11×3−1+2 |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 198 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,15)(13,14)(17,20,21)(19,23,24);(13,14,15)(16,17,19,18,21,23,22,20,24)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 47);