Finite Group DatabasebetaFinite Group Databasebeta| order | 6050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5×C11 |
| unambiguous semidirect product | C5⋊(C5⋊(C11⋊D11)) |
| unambiguous semidirect product | C11⋊(C5⋊D55) |
| Fitting, socle, derived, Hall | C52×C112 ⋊ C2 |
| Sylow | C112 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C112 | C2 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 | |
224 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,11^2|b^a=b^4,c^a=c^4,d^a=d^10,e^a=e^101514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6050, 80);