Finite Group DatabasebetaFinite Group Databasebeta| order | 9702 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting | C3×C11×C49 ⋊ C2×C3 |
| derived, Hall | C11×C49 ⋊ C2×C32 |
| Hall | C3×C11×C49⋊C3 ⋊ C2 |
| Hall | D539 ⋊ C32 |
| Hall | C3×C49⋊C3 ⋊ D11 |
| Sylow | C49 ⋊ C32×D11 |
| Sylow | C11 ⋊ C3×D49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C11⋊(D49⋊C3) |
| commutator, cosocle, hypocenter | C11×C49 | C2×C32 |
| Frattini | C7 | C3×C11⋊AGL(1,𝔽7) |
| Fitting | C3×C11×C49 | C2×C3 |
| socle | C3×C7×C11 | AGL(1,𝔽7) |
| LCS | G ▷ C11×C49 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
327 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D11×D49⋊C3, D3×C11⋊(D49⋊C3), D33⋊(D49⋊C3), … |
| maximal normal subgroup of | C3×D11×D49⋊C3, D3×C11⋊(D49⋊C3), D33⋊(D49⋊C3), … |
| maximal quotient of | C3×C11⋊((C49⋊C3)⋊C4), C2×C3×C11⋊(D49⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9702, 16);