Finite Group DatabasebetaFinite Group Databasebeta| order | 9702 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C7 |
| direct product | C11×#11725078 |
| derived, Sylow | C72 ⋊ C2×C9×C11 |
| Hall | C11×#89205 ⋊ C2 |
| Hall | C11×C7⋊D7 ⋊ C9 |
| Hall | C72×C11 ⋊ C2×C9 |
| Hall | #89205 ⋊ C2×C11 |
| Hall | C7⋊D7 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | #64425 |
| commutator, hypocenter | C72 | C2×C9×C11 |
| Frattini | C3 | C11×#64425 |
| Fitting, socle | C3×C72×C11 | C2×C3 |
| prime radical | C3×C11×C7⋊D7 | C3 |
| cosocle | C3×C72 | C2×C3×C11 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C11 | |
64 conjugacy classes of subgroups.
462 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#11725078, C11×#11725075⋊C2, #34084664, … |
| maximal normal subgroup of | D11×#11725078, C11×#11725075⋊C2, #34084664, … |
| maximal quotient of | C11×#13183534, C2×C11×#11725078 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9702, 39);