Finite Group DatabasebetaFinite Group Databasebeta| order | 9724 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13×C17 · Schur multiplier (H2) = C1 |
| direct product | C13×C17×Dic11 |
| unambiguous semidirect product | C11⋊(C4×C13×C17) |
| derived, Sylow | C11 ⋊ C4×C13×C17 |
| Hall | C11×C13×C17 ⋊ C4 |
| Hall | C11×C17 ⋊ C4×C13 |
| Hall | C11×C13 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13×C17 | D11 |
| commutator, hypocenter | C11 | C4×C13×C17 |
| Frattini | C2 | C13×C17×D11 |
| Fitting, socle, prime radical | C2×C11×C13×C17 | C2 |
| cosocle | C2×C11 | C2×C13×C17 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C13×C17 | |
24 conjugacy classes of subgroups.
3094 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×C17×Dic11, C13×C17×Dic33, C17×C13⋊C3×Dic11 |
| maximal normal subgroup of | C3×C13×C17×Dic11, C17×C13⋊C3×Dic11 |
| maximal quotient of | C3×C13×C17×Dic11, C13×C17×Dic33 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9724, 5);