Finite Group DatabasebetaFinite Group Databasebeta| order | 9702 |
| automorphism | Aut(G) order 12224520 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4851 |
| unambiguous semidirect product | C9⋊D539 |
| unambiguous semidirect product | C11⋊D441 |
| unambiguous semidirect product | C49⋊D99 |
| Fitting, derived, Hall | C9×C11×C49 ⋊ C2 |
| Hall | C11×C49 ⋊ D9 |
| Hall | C9×C49 ⋊ D11 |
| Hall | C9×C11 ⋊ D49 |
| Sylow | C49 ⋊ D99 |
| Sylow | C11 ⋊ D441 |
| Sylow | C9 ⋊ D539 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C11×C49 | C2 |
| Frattini | C3×C7 | D231 |
| socle | C3×C7×C11 | D21 |
| LCS | G ▷ C9×C11×C49 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,11,3,7|b^3=e^2,c^7=f^6,b^a=b^2e,c^a=c^6f,d^a=d^10,e^a=e^2,f^a=f^62427 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D441, D49×D99, D9×D539, … |
| maximal normal subgroup of | D11×D441, D49×D99, D9×D539, … |
| maximal quotient of | Dic4851, C2×D4851, D14553 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9702, 12);