Finite Group DatabasebetaFinite Group Databasebeta| order | 6050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D605 |
| unambiguous semidirect product | C5⋊(C5×D121) |
| Fitting, Hall | C52×C121 ⋊ C2 |
| derived | C5×C121 ⋊ C2×C5 |
| Sylow | C121 ⋊ C5×D5 |
| Sylow | C52 ⋊ D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D605 |
| commutator, hypocenter | C5×C121 | C2×C5 |
| Frattini | C11 | C5×D55 |
| Fitting | C52×C121 | C2 |
| socle | C52×C11 | D11 |
| LCS | G ▷ C5×C121 | |
| UCS | C1 ◁ C5 | |
30 conjugacy classes of subgroups.
1520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D5×D121, D5×D605, (C5⋊D5)⋊D121, … |
| maximal normal subgroup of | C5×D5×D121, D5×D605, (C5⋊D5)⋊D121, … |
| maximal quotient of | C5×Dic605, C2×C5×D605, C3×C5×D605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6050, 14);