Finite Group DatabasebetaFinite Group Databasebeta| order | 9702 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C11⋊#64422 |
| unambiguous semidirect product | C11⋊(C3×#64422) |
| Fitting, socle | C3×C72×C11 ⋊ C2×C3 |
| derived, Hall | C72×C11 ⋊ C2×C32 |
| Hall | C3×C11×#3862 ⋊ C2 |
| Hall | C7×D77 ⋊ C32 |
| Hall | C3×#3862 ⋊ D11 |
| Sylow | C72 ⋊ C32×D11 |
| Sylow | C11 ⋊ C3×#64422 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C11⋊#64422 |
| commutator, cosocle, hypocenter | C72×C11 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C11 | C2×C3 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C3 | |
100 conjugacy classes of subgroups.
336 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#64422⋊D11, C3×#20266343, C3×D11×#64422, … |
| maximal normal subgroup of | C3×#64422⋊D11, C3×#20266343, C3×D11×#64422, … |
| maximal quotient of | C3×C11⋊#10596872, C2×C3×C11⋊#64422 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9702, 86);