Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C9 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C9×AGL(1,𝔽7) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C23×C9) |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊(C22×C9) |
| Fitting | C22×C7×C9 ⋊ C2×C3 |
| derived, Sylow | C7 ⋊ C23×C3×C9 |
| Hall | C9×ΓL(1,𝔽8) ⋊ C23 |
| Hall | C22×D7 ⋊ C3×C9 |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D9×AGL(1,𝔽7), C22×3−1+2×AGL(1,𝔽7), D4×C9×AGL(1,𝔽7), … |
| maximal normal subgroup of | C22×D9×AGL(1,𝔽7), C22×3−1+2×AGL(1,𝔽7), D4×C9×AGL(1,𝔽7), … |
| maximal quotient of | D4×C9×AGL(1,𝔽7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 504);