Finite Group DatabasebetaFinite Group Databasebeta| order | 9724 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×Dic143 |
| unambiguous semidirect product | C11⋊(C17×Dic13) |
| derived, Hall | C11×C13 ⋊ C4×C17 |
| Hall | C11×C13×C17 ⋊ C4 |
| Hall | C13×C17 ⋊ Dic11 |
| Hall | C11×C17 ⋊ Dic13 |
| Sylow | C13 ⋊ C17×Dic11 |
| Sylow | C11 ⋊ C17×Dic13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D143 |
| commutator, hypocenter | C11×C13 | C4×C17 |
| Frattini | C2 | C17×D143 |
| Fitting, socle, prime radical | C2×C11×C13×C17 | C2 |
| cosocle | C2×C11×C13 | C2×C17 |
| LCS | G ▷ C11×C13 | |
| UCS | C1 ◁ C2×C17 | |
24 conjugacy classes of subgroups.
2482 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C17×Dic143, C17×Dic429, C17×C11⋊(Dic13⋊C3) |
| maximal normal subgroup of | C3×C17×Dic143, C17×C11⋊(Dic13⋊C3) |
| maximal quotient of | C3×C17×Dic143, C17×Dic429 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9724, 7);