Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C37 · Schur multiplier (H2) = C2 |
| direct product | D3×C7×D7×C37 |
| unambiguous semidirect product | (D3×C7)⋊(C2×C7×C37) |
| unambiguous semidirect product | (C3×D7)⋊(C2×C7×C37) |
| unambiguous semidirect product | D21⋊(C2×C7×C37) |
| Fitting, socle, Hall | C3×C72×C37 ⋊ C22 |
| derived | C3×C7 ⋊ C22×C7×C37 |
| Hall | C72×C37 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C22×C37 |
| Hall | C3×C37 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ C2×D3×C37 |
| Sylow | C3 ⋊ C2×C7×D7×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C37 | D3×D7 |
| commutator, cosocle, hypocenter | C3×C7 | C22×C7×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C37 | C22 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C7×C37 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1554 |
3885 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 331);