Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×C4⋊Dic9 |
| unambiguous semidirect product | C4⋊(C11×Dic9) |
| Hall | C9×C11 ⋊ C4⋊C4 |
| Sylow | C9 ⋊ C11×C4⋊C4 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 1584 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,17,19,18,13,15,14,20,16)(25,26,27,28);(13,15)(14,18)(16,17)(19,20)(21,22,23,24)(26,28)462 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 56);