Finite Group DatabasebetaFinite Group Databasebeta| order | 6050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C5 |
| direct product | C11×C5⋊D55 |
| unambiguous semidirect product | C5⋊(C11×D55) |
| unambiguous semidirect product | C11⋊(C11×C5⋊D5) |
| Fitting, socle, Hall | C52×C112 ⋊ C2 |
| derived | C52×C11 ⋊ C2×C11 |
| Sylow | C112 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C5⋊D55 |
| commutator, hypocenter | C52×C11 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C112 | C2 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 ◁ C11 | |
104 conjugacy classes of subgroups.
1529 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D11×C5⋊D5, D11×C5⋊D55, #27130989, … |
| maximal normal subgroup of | C11×D11×C5⋊D5, D11×C5⋊D55, #27130989, … |
| maximal quotient of | C11×C11⋊#1039, C2×C11×C5⋊D55, C11×C3⋊(C5⋊D55), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6050, 79);