Finite Group DatabasebetaFinite Group Databasebeta| order | 9702 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D11×C49⋊C3 |
| unambiguous semidirect product | C11⋊(C2×C3×C49⋊C3) |
| unambiguous semidirect product | (D11×C49)⋊C32 |
| unambiguous semidirect product | (C3×D11×C49)⋊C3 |
| Fitting | C3×C11×C49 ⋊ C2×C3 |
| derived, Hall | C11×C49 ⋊ C2×C32 |
| Hall | C3×C11×C49⋊C3 ⋊ C2 |
| Hall | D11×C49 ⋊ C32 |
| Sylow | C49 ⋊ C32×D11 |
| Sylow | C11 ⋊ C2×C3×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D11×C49⋊C3 |
| commutator, cosocle, hypocenter | C11×C49 | C2×C32 |
| Frattini | C7 | C3×ΓL(1,𝔽8)×D11 |
| Fitting | C3×C11×C49 | C2×C3 |
| socle | C3×C7×C11 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C11×C49 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
399 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D11×D49⋊C3, D11×C3⋊(D49⋊C3), D3×D11×C49⋊C3, … |
| maximal normal subgroup of | C3×D11×D49⋊C3, D11×C3⋊(D49⋊C3), D3×D11×C49⋊C3, … |
| maximal quotient of | C3×Dic11×C49⋊C3, C2×C3×D11×C49⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9702, 14);