Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of AGL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×C9×AGL(1,𝔽8) |
| unambiguous semidirect product | (C23×C3×C9)⋊C7 |
| Fitting, Hall | C23×C3×C9 ⋊ C7 |
| derived, Sylow | C23 ⋊ C3×C7×C9 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3)(14,15,16,18,20,17,19);(4,5,6,7,8,9,10,11,12)(13,17)(14,15)(16,20)(18,19)216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 487);