Finite Group DatabasebetaFinite Group Databasebeta| order | 21758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D989 |
| unambiguous semidirect product | C43⋊(C11×D23) |
| Fitting, socle, Hall | C11×C23×C43 ⋊ C2 |
| derived, Hall | C23×C43 ⋊ C2×C11 |
| Hall | C11×C43 ⋊ D23 |
| Hall | C11×C23 ⋊ D43 |
| Sylow | C43 ⋊ C11×D23 |
| Sylow | C23 ⋊ C11×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D989 |
| commutator, cosocle, hypocenter | C23×C43 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C23×C43 | C2 |
| LCS | G ▷ C23×C43 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
5456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×D989, C11×D2967, C11×C23⋊(D43⋊C3) |
| maximal normal subgroup of | C3×C11×D989, C11×C23⋊(D43⋊C3) |
| maximal quotient of | C3×C11×D989, C11×D2967 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21758, 5);