Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D49×D111 |
| unambiguous semidirect product | (C3×D49)⋊D37 |
| unambiguous semidirect product | (C37×D49)⋊D3 |
| Fitting, derived, Hall | C3×C37×C49 ⋊ C22 |
| Hall | C37×C49 ⋊ C2×D3 |
| Hall | C3×C49 ⋊ C2×D37 |
| Hall | C3×C37 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×D111 |
| Sylow | C37 ⋊ D3×D49 |
| Sylow | C3 ⋊ D37×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C37×C49 | C22 |
| Frattini | C7 | D7×D111 |
| socle | C3×C7×C37 | C2×D7 |
| LCS | G ▷ C3×C37×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5439 |
1482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 58);