Finite Group DatabasebetaFinite Group Databasebeta| order | 2640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | D3×(C11⋊C5)⋊C8 |
| derived, Hall | C3×C11 ⋊ C2×C5×C8 |
| Hall | D3×C11⋊C8 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C2×C8 |
| Hall | C11⋊C5 ⋊ D3×C8 |
| Sylow | C11 ⋊ C5×D3×C8 |
| Sylow | C3 ⋊ C2×(C11⋊C5)⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×AGL(1,𝔽11) |
| commutator, hypocenter | C3×C11 | C2×C5×C8 |
| Fitting, cosocle | C3×C4×C11 | C22×C5 |
| socle | C2×C3×C11 | C2×C4×C5 |
| prime radical | C2×D3×C11⋊C5 | C4 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C4 | |
88 conjugacy classes of subgroups.
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C8×AGL(1,𝔽11), D3×#4313⋊C5, D3×#4318⋊C5, … |
| maximal normal subgroup of | D3×C8×AGL(1,𝔽11), D3×#4313⋊C5, D3×#4318⋊C5, … |
Past the SmallGroups library coverage — no SmallGroups id.