Finite Group DatabasebetaFinite Group Databasebeta| order | 2124 |
| isoclinism | isoclinic class of D9×D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D9×D59 |
| unambiguous semidirect product | (D9×C59)⋊C2 |
| unambiguous semidirect product | (C9×D59)⋊C2 |
| unambiguous semidirect product | D531⋊C2 |
| Fitting, derived, Hall | C9×C59 ⋊ C22 |
| Sylow | C59 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C59 | C22 |
| Frattini | C3 | D3×D59 |
| socle | C3×C59 | C2×D3 |
| LCS | G ▷ C9×C59 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 68 |
| transitive degree | μt(G) = 531 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D9×D59, D59×D63, D9×D413, … |
| maximal normal subgroup of | C7×D9×D59, C11×D9×D59, C13×D9×D59, … |
| maximal quotient of | C7×D9×D59, D59×D63, D9×D413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2124, 6);