Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C9⋊C8) |
| derived | C7×C9 ⋊ C3×C8 |
| Hall | C9×ΓL(1,𝔽8) ⋊ C8 |
| Sylow | C7 ⋊ C3×C9⋊C8 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2,3,2^2,3,7,3|a^2=c,c^2=d,e^3=g,e^a=e^2g^2,f^a=f^6,g^a=g^2,f^b=f^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 53);