Finite Group DatabasebetaFinite Group Databasebeta| order | 9702 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#11725076 |
| derived, Hall | C72×C11 ⋊ C2×C9 |
| Hall | C11×#89204 ⋊ C2 |
| Hall | C7×D77 ⋊ C9 |
| Hall | #89204 ⋊ D11 |
| Sylow | C72 ⋊ C9×D11 |
| Sylow | C11 ⋊ #11725076 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C11⋊#64423 |
| commutator, hypocenter | C72×C11 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C11 | C2×C3 |
| prime radical | C3×C7×D77 | C3 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C3 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7^2,11,3|b^3=f,c^a=c^6,e^a=e^10,c^b=c^2,d^b=d^2336 conjugacy classes — view the full character table.
| maximal subgroup of | #11725076⋊D11, #11725077⋊D11, D11×#11725076, … |
| maximal normal subgroup of | #11725076⋊D11, #11725077⋊D11, D11×#11725076, … |
| maximal quotient of | C11⋊#13183532, C2×C11⋊#11725076 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9702, 42);