Finite Group DatabasebetaFinite Group Databasebeta| order | 9702 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | D3×C11×C49⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C11×C49⋊C3) |
| unambiguous semidirect product | (D3×C49)⋊(C3×C11) |
| unambiguous semidirect product | (D3×C11×C49)⋊C3 |
| Fitting | C3×C11×C49 ⋊ C2×C3 |
| derived | C3×C49 ⋊ C2×C3×C11 |
| Hall | C3×C11×C49⋊C3 ⋊ C2 |
| Hall | C11×C49 ⋊ C3×D3 |
| Hall | C3×C49⋊C3 ⋊ C2×C11 |
| Sylow | C49 ⋊ C3×D3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D3×C49⋊C3 |
| commutator, cosocle, hypocenter | C3×C49 | C2×C3×C11 |
| Frattini | C7 | D3×C11×ΓL(1,𝔽8) |
| Fitting | C3×C11×C49 | C2×C3 |
| socle | C3×C7×C11 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C3×C49 | |
| UCS | C1 ◁ C11 | |
54 conjugacy classes of subgroups.
627 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C11×D49⋊C3, D3×C11⋊(D49⋊C3), D3×D11×C49⋊C3, … |
| maximal normal subgroup of | D3×C11×D49⋊C3, D3×C11⋊(D49⋊C3), D3×D11×C49⋊C3, … |
| maximal quotient of | C11×Dic3×C49⋊C3, C2×D3×C11×C49⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9702, 17);