Finite Group DatabasebetaFinite Group Databasebeta| order | 6050 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C11 · Schur multiplier (H2) = C5 |
| direct product | C2×C5×C11×C11⋊C5 |
| unambiguous semidirect product | (C2×C11)⋊(C52×C11) |
| unambiguous semidirect product | (C2×C5×C11)⋊(C5×C11) |
| Fitting, socle | C2×C5×C112 ⋊ C5 |
| derived | C11 ⋊ C2×C52×C11 |
| Hall | C2×C112 ⋊ C52 |
| Sylow | C112 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C11 | C11⋊C5 |
| commutator, hypocenter | C11 | C2×C52×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C112 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C5×C11 | |
72 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6050, 69);