Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×D11×C3⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (D11×C11⋊C5)⋊(C3×D3) |
| Fitting, socle, Hall | C32×C112 ⋊ C22×C5 |
| derived | C3×C112 ⋊ C22×C3×C5 |
| Hall | C32×C11×C11⋊C5 ⋊ C22 |
| Hall | C3×D11×D33 ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ C2×C3×D3 |
| Sylow | C112 ⋊ C2×C3×C5×D3 |
| Sylow | C32 ⋊ D11×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D11×C3⋊AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C3×C112 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C112 | C22×C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C3 | |
185 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 185 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
378 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 440);