Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37×C49 · Schur multiplier (H2) = C1 |
| direct product | D3×C37×C49 |
| unambiguous semidirect product | C3⋊(C2×C37×C49) |
| Fitting, Hall | C3×C37×C49 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C37×C49 |
| Hall | C3×C49 ⋊ C2×C37 |
| Hall | C3×C37 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37×C49 | D3 |
| commutator, hypocenter | C3 | C2×C37×C49 |
| Frattini | C7 | D3×C7×C37 |
| Fitting | C3×C37×C49 | C2 |
| socle | C3×C7×C37 | C2×C7 |
| prime radical | D3×C7×C37 | C7 |
| cosocle | C3×C7 | C2×C7×C37 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C37×C49 | |
24 conjugacy classes of subgroups.
5439 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C49×D37, D3×C37×D49, D3×D1813, … |
| maximal normal subgroup of | D3×C49×D37, D3×C37×D49, D3×D1813, … |
| maximal quotient of | Dic3×C37×C49, C2×D3×C37×C49, D9×C37×C49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 21);