Finite Group DatabasebetaFinite Group Databasebeta| order | 10550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D211⋊C5) |
| unambiguous semidirect product | (C211⋊C5)⋊D5 |
| unambiguous semidirect product | D1055⋊C5 |
| Fitting, socle, derived | C5×C211 ⋊ C2×C5 |
| Hall | C5×C211⋊C5 ⋊ C2 |
| Sylow | C211 ⋊ C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C211 | C2×C5 |
| LCS | G ▷ C5×C211 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,211|c^a=c^4,d^a=d^210,d^b=d^188125 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10550, 9);