Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | #121×AGL(1,𝔽11) |
| Fitting | C11×#121 ⋊ C2×C5 |
| Hall | D11×#121 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×#121 |
| Sylow | C11 ⋊ C2×C5×#121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×AGL(1,𝔽11) |
| commutator, socle, cosocle | C22×C11 | C24×C5 |
| Fitting | C11×#121 | C2×C5 |
| hypercenter | #121 | AGL(1,𝔽11) |
| hypocenter | C11 | C2×C5×#121 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ #121 | |
852 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | #525×AGL(1,𝔽11), #535×AGL(1,𝔽11), #532×AGL(1,𝔽11), … |
| maximal normal subgroup of | #525×AGL(1,𝔽11), #535×AGL(1,𝔽11), #532×AGL(1,𝔽11), … |
| maximal quotient of | #469×AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.