Finite Group DatabasebetaFinite Group Databasebeta| order | 1232 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×(C2×D11)⋊C4 |
| unambiguous semidirect product | (C2×D11)⋊(C4×C7) |
| Fitting | C2×C4×C7×C11 ⋊ C2 |
| Hall | C7×C11 ⋊ C22⋊C4 |
| Sylow | C11 ⋊ C7×C22⋊C4 |
68 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)(8,9,11,13,15,17,18,16,14,12,10)(19,20,21,22)(24,26);(9,10)(11,12)(13,14)(15,16)(17,18)(23,24)(25,26)350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1232, 40);