Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C27 |
| direct product | #120×AGL(1,𝔽11) |
| Fitting | C11×#120 ⋊ C2×C5 |
| Hall | D11×#120 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×#120 |
| Sylow | C11 ⋊ C2×C5×#120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×AGL(1,𝔽11) |
| commutator, socle, cosocle | C22×C11 | C24×C5 |
| Fitting | C11×#120 | C2×C5 |
| hypercenter | #120 | AGL(1,𝔽11) |
| hypocenter | C11 | C2×C5×#120 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ #120 | |
1324 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 236 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
154 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.