Finite Group DatabasebetaFinite Group Databasebeta| order | 6050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D121⋊C25 |
| unambiguous semidirect product | (C121⋊C25)⋊C2 |
| derived, Sylow | C121 ⋊ C2×C25 |
| Hall | C121⋊C25 ⋊ C2 |
| Hall | D121 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D121⋊C5 |
| commutator, hypocenter | C121 | C2×C25 |
| Frattini, socle | C5×C11 | AGL(1,𝔽11) |
| Fitting | C5×C121 | C2×C5 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C5 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11,5,11|b^5=d,c^11=e^10,c^a=c^10e,e^a=e^10,c^b=c^4e^4,e^b=e^4110 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D121⋊C25, C3×D121⋊C25, C3⋊(D121⋊C25) |
| maximal normal subgroup of | C2×D121⋊C25, C3×D121⋊C25 |
| maximal quotient of | Dic121⋊C25, C2×D121⋊C25, C3×D121⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6050, 2);