Finite Group DatabasebetaFinite Group Databasebeta| order | 1232 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#1142 |
| Hall | C7×C11 ⋊ SD16 |
| Sylow | C7 ⋊ C11×SD16 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 616 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,17,18,16,14)(20,23)(21,26)(24,25);(13,14)(15,16)(17,18)(19,20,22,25)(21,23,26,24)242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1232, 58);