Finite Group DatabasebetaFinite Group Databasebeta| order | 11466 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#16838420 |
| Fitting | C3×C13×C49 ⋊ C2×C3 |
| derived, Hall | C13×C49 ⋊ C2×C32 |
| Hall | C3×#14274255 ⋊ C2 |
| Hall | D637 ⋊ C32 |
| Sylow | C49 ⋊ C3×D13⋊C3 |
| Sylow | C13 ⋊ C3×D49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16838420 |
| commutator, cosocle, hypocenter | C13×C49 | C2×C32 |
| Frattini | C7 | C3×#10587723 |
| Fitting | C3×C13×C49 | C2×C3 |
| socle | C3×C7×C13 | AGL(1,𝔽7) |
| LCS | G ▷ C13×C49 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
336 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#16838414⋊C2, D3×#16838420, #16838420⋊D3, … |
| maximal normal subgroup of | C3×#16838414⋊C2, D3×#16838420, #16838420⋊D3, … |
| maximal quotient of | C3×#21439444, C2×C3×#16838420 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11466, 40);