Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#3710 |
| derived, Sylow | C32 ⋊ C2×C8×C11 |
| Hall | C32×C11 ⋊ C2×C8 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 264 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,14,15,19,16,13,17,18)(21,22)(23,24,25);(12,13,15,18,16,14,17,19)(20,21,22)(24,25)396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 219);