Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C8 · Schur multiplier (H2) = C1 |
| direct product | C7×3−1+2⋊C8 |
| unambiguous semidirect product | 3−1+2⋊(C7×C8) |
| unambiguous semidirect product | (C9⋊C8)⋊(C3×C7) |
| derived | C9 ⋊ C3×C7×C8 |
| Hall | C7×3−1+2 ⋊ C8 |
| Sylow | 3−1+2 ⋊ C7×C8 |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 504 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5,6,7)(9,13,16,11,12,15)(10,14)(17,18,19,21,20,22,23,24);(8,16,11,14,12,13,10,9,15)280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 70);