Finite Group DatabasebetaFinite Group Databasebeta| order | 1232 |
| isoclinism | isoclinic class of #4314 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D88 |
| Fitting | C7×C8×C11 ⋊ C2 |
| Hall | C7×C11 ⋊ D8 |
| Sylow | C11 ⋊ C7×D8 |
44 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)(8,9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26);(9,15)(10,14)(11,13)(17,26)(18,25)(19,24)(20,23)(21,22)329 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1232, 33);