Finite Group DatabasebetaFinite Group Databasebeta| order | 44000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | AGL(1,𝔽5)2×AGL(1,𝔽11) |
| Fitting, socle, derived | C52×C11 ⋊ C2×C42×C5 |
| Hall | C52×C11⋊C5 ⋊ C2×C42 |
| Sylow | C11 ⋊ C2×C5×AGL(1,𝔽5)2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C11 | C2×C42×C5 |
| prime radical | D52×AGL(1,𝔽11) | C22 |
| cosocle | D52×C11 | C23×C5 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 | |
968 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
275 conjugacy classes. The character table is too large to display.
| holomorph of | C11×AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.