Finite Group DatabasebetaFinite Group Databasebeta| order | 2640 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C2 |
| direct product | SL(2,ℤ/4)×C11⋊C5 |
| derived | C11×A4 ⋊ C4×C5 |
| Hall | C11×SL(2,ℤ/4) ⋊ C5 |
| Sylow | C11 ⋊ C5×SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | S4×C11⋊C5 |
| commutator, hypocenter | C11×A4 | C4×C5 |
| Fitting, socle | C23×C11 | C5×D3 |
| prime radical | C2×A4×C11⋊C5 | C2 |
| cosocle | C2×C11×A4 | C2×C5 |
| LCS | G ▷ C11×A4 | |
| UCS | C1 ◁ C2 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊C5×GL(2,ℤ/4) |
| maximal normal subgroup of | C11⋊C5×GL(2,ℤ/4) |
Past the SmallGroups library coverage — no SmallGroups id.