Finite Group DatabasebetaFinite Group Databasebeta| order | 9724 |
| automorphism | Aut(G) order 9335040 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4862 |
| direct product | C2×D2431 |
| unambiguous semidirect product | (C2×C11)⋊D221 |
| unambiguous semidirect product | (C2×C13)⋊D187 |
| unambiguous semidirect product | (C2×C17)⋊D143 |
| Fitting, socle | C2×C11×C13×C17 ⋊ C2 |
| derived, Hall | C11×C13×C17 ⋊ C22 |
| Hall | C13×C17 ⋊ C2×D11 |
| Hall | C11×C17 ⋊ C2×D13 |
| Hall | C11×C13 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D143 |
| Sylow | C13 ⋊ C2×D187 |
| Sylow | C11 ⋊ C2×D221 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2431 |
| commutator, cosocle, hypocenter | C11×C13×C17 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C13×C17 | C2 |
| LCS | G ▷ C11×C13×C17 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2434 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11⋊(C17⋊(D13⋊C3)), D3×D2431, C2×C3×D2431, … |
| maximal normal subgroup of | C2×C11⋊(C17⋊(D13⋊C3)), C2×C3×D2431, D9724 |
| maximal quotient of | D3×D2431, C2×C3×D2431, C2×D7293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9724, 29);