Finite Group DatabasebetaFinite Group Databasebeta| order | 882 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | D9×C49 |
| unambiguous semidirect product | C9⋊(C2×C49) |
| Fitting, Hall | C9×C49 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D9 |
| commutator, hypocenter | C9 | C2×C49 |
| Frattini, socle | C3×C7 | D3×C7 |
| Fitting | C9×C49 | C2 |
| prime radical | C7×D9 | C7 |
| cosocle | C7×C9 | C2×C7 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C49 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 441 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D49, C2×D9×C49, C5×D9×C49, … |
| maximal normal subgroup of | D9×D49, C2×D9×C49, C5×D9×C49, … |
| maximal quotient of | Dic9×C49, C2×D9×C49, C5×D9×C49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(882, 3);