Finite Group DatabasebetaFinite Group Databasebeta| order | 6050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D605 |
| unambiguous semidirect product | C121⋊(C5⋊D5) |
| Fitting, derived, Hall | C52×C121 ⋊ C2 |
| Sylow | C121 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C121 | C2 |
| Frattini | C11 | C5⋊D55 |
| socle | C52×C11 | D11 |
| LCS | G ▷ C52×C121 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,11^2|d^11=e^10,b^a=b^4,c^a=c^4,d^a=d^10e,e^a=e^101514 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5⋊D5×D121, D5×D605, C2×C5⋊D605, … |
| maximal normal subgroup of | C5⋊D5×D121, D5×D605, C2×C5⋊D605, … |
| maximal quotient of | C121⋊#1039, C2×C5⋊D605, C3×C5⋊D605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6050, 16);