Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8×C9 · Schur multiplier (H2) = C3 |
| direct product | C9×ΓL(1,𝔽8)⋊C8 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C8×C9) |
| derived, Sylow | C7 ⋊ C3×C8×C9 |
| Hall | C9×ΓL(1,𝔽8) ⋊ C8 |
| Hall | C7⋊C8 ⋊ C3×C9 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 42);