Finite Group DatabasebetaFinite Group Databasebeta| order | 882 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D49 |
| Fitting, Hall | C9×C49 ⋊ C2 |
| derived, Sylow | C49 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D49 |
| commutator, hypocenter | C49 | C2×C9 |
| Frattini, socle | C3×C7 | C3×D7 |
| Fitting | C9×C49 | C2 |
| prime radical | C3×D49 | C3 |
| cosocle | C3×C49 | C2×C3 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C9 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 441 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D49, C2×C9×D49, C5×C9×D49, … |
| maximal normal subgroup of | D9×D49, C2×C9×D49, C5×C9×D49, … |
| maximal quotient of | C9×Dic49, C2×C9×D49, C5×C9×D49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(882, 4);