Finite Group DatabasebetaFinite Group Databasebeta| order | 882 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1 |
| direct product | C3×D3×C49 |
| unambiguous semidirect product | C3⋊(C2×C3×C49) |
| Fitting, Hall | C32×C49 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C49 |
| Sylow | C32 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C49 | D3 |
| commutator, hypocenter | C3 | C2×C3×C49 |
| Frattini | C7 | C3×D3×C7 |
| Fitting | C32×C49 | C2 |
| socle | C32×C7 | C2×C7 |
| prime radical | C3×D3×C7 | C7 |
| cosocle | C3×C7 | C2×C3×C7 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C49 | |
27 conjugacy classes of subgroups.
| transitive degree | μt(G) = 294 |
441 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×D49, D32×C49, D3×D147, … |
| maximal normal subgroup of | C3×D3×D49, D32×C49, D3×D147, … |
| maximal quotient of | C3×Dic3×C49, C2×C3×D3×C49, C3×C5×D3×C49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(882, 12);