Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×C4⋊Dic11 |
| unambiguous semidirect product | C4⋊(C32×Dic11) |
| Hall | C32×C11 ⋊ C4⋊C4 |
| Sylow | C11 ⋊ C32×C4⋊C4 |
156 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 1584 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3)(7,8,10,12,14,16,17,15,13,11,9)(22,23,24,25);(4,5,6)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19,20,21)(23,25)450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 285);