Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D7×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D7×D9 |
| unambiguous semidirect product | (C7×D9)⋊C23 |
| unambiguous semidirect product | (C9×D7)⋊C23 |
| unambiguous semidirect product | D63⋊C23 |
| Fitting | C22×C7×C9 ⋊ C22 |
| derived, Hall | C7×C9 ⋊ C24 |
| Sylow | C9 ⋊ C23×D7 |
| Sylow | C7 ⋊ C23×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D7×D9 |
| commutator, cosocle, hypocenter | C7×C9 | C24 |
| Frattini | C3 | C22×D3×D7 |
| Fitting | C22×C7×C9 | C22 |
| socle | C22×C3×C7 | C2×D3 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C22 | |
402 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D9×AGL(1,𝔽7), C22×D7×AGL(1,ℤ/9), C22×#67355⋊C2, … |
| maximal normal subgroup of | C22×D9×AGL(1,𝔽7), C22×D7×AGL(1,ℤ/9), C22×#67355⋊C2, … |
| maximal quotient of | D4×D7×D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 507);