Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C49 · Schur multiplier (H2) = C2 |
| direct product | D3×C49×D37 |
| unambiguous semidirect product | (D3×C37)⋊(C2×C49) |
| unambiguous semidirect product | (C3×D37)⋊(C2×C49) |
| unambiguous semidirect product | D111⋊(C2×C49) |
| Fitting, Hall | C3×C37×C49 ⋊ C22 |
| derived, Hall | C3×C37 ⋊ C22×C49 |
| Hall | C37×C49 ⋊ C2×D3 |
| Hall | C3×C49 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D3×C49 |
| Sylow | C3 ⋊ C2×C49×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D3×D37 |
| commutator, hypocenter | C3×C37 | C22×C49 |
| Frattini | C7 | D3×C7×D37 |
| Fitting | C3×C37×C49 | C22 |
| socle, cosocle | C3×C7×C37 | C22×C7 |
| prime radical | D3×C7×D37 | C7 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C49 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5439 |
2940 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 54);