Finite Group DatabasebetaFinite Group Databasebeta| order | 6050 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C121 · Schur multiplier (H2) = C5 |
| direct product | C5⋊D5×C121 |
| unambiguous semidirect product | C5⋊(D5×C121) |
| Fitting, Hall | C52×C121 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | C5⋊D5 |
| commutator, hypocenter | C52 | C2×C121 |
| Frattini | C11 | C11×C5⋊D5 |
| Fitting | C52×C121 | C2 |
| socle | C52×C11 | C2×C11 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C121 | |
48 conjugacy classes of subgroups.
1694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1043×C121, C121⋊#1043, #1044×C121, … |
| maximal normal subgroup of | #1043×C121, C121⋊#1043, #1044×C121, … |
| maximal quotient of | #1039×C121, C2×C5⋊D5×C121, C3×C5⋊D5×C121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6050, 15);