Finite Group DatabasebetaFinite Group Databasebeta| order | 1764 |
| isoclinism | isoclinic class of D9×D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D9×D49 |
| unambiguous semidirect product | (D9×C49)⋊C2 |
| unambiguous semidirect product | (C9×D49)⋊C2 |
| unambiguous semidirect product | D441⋊C2 |
| Fitting, derived, Hall | C9×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C49 | C22 |
| Frattini, socle | C3×C7 | D3×D7 |
| LCS | G ▷ C9×C49 | |
| UCS | C1 | |
45 conjugacy classes of subgroups.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 441 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C11×D9×D49, D49×D99, D9×D539, … |
| maximal normal subgroup of | C11×D9×D49, C13×D9×D49, C17×D9×D49, … |
| maximal quotient of | C11×D9×D49, D49×D99, D9×D539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1764, 8);