Finite Group DatabasebetaFinite Group Databasebeta| order | 756 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C9×AGL(1,𝔽7) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C22×C9) |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊(C2×C9) |
| Fitting | C2×C7×C9 ⋊ C2×C3 |
| derived, Sylow | C7 ⋊ C22×C3×C9 |
| Hall | C9×ΓL(1,𝔽8) ⋊ C22 |
| Hall | C2×D7 ⋊ C3×C9 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(756, 70);