Finite Group DatabasebetaFinite Group Databasebeta| order | 55660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽11)×AGL(1,𝔽23) |
| Fitting, socle, derived | C11×C23 ⋊ C22×C5×C11 |
| Hall | C11⋊C5×C23⋊C11 ⋊ C22 |
| Hall | D11×AGL(1,𝔽23) ⋊ C5 |
| Hall | C11×C23⋊C11 ⋊ C22×C5 |
| Sylow | C23 ⋊ C2×C11×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C23 | C22×C5×C11 |
| LCS | G ▷ C11×C23 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 253 |
253 conjugacy classes — view the full character table.
| holomorph of | C11×C23 |
Past the SmallGroups library coverage — no SmallGroups id.