Finite Group DatabasebetaFinite Group Databasebeta| order | 10550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C2×C211⋊C25 |
| unambiguous semidirect product | (C2×C211)⋊C25 |
| derived, Sylow | C211 ⋊ C2×C25 |
| Hall | C2×C211 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C211⋊C5 |
| commutator, hypocenter | C211 | C2×C25 |
| Frattini | C5 | C2×C211⋊C5 |
| Fitting, socle, prime radical | C2×C5×C211 | C5 |
| cosocle | C5×C211 | C2×C5 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C2×C5 | |
12 conjugacy classes of subgroups.
470 conjugacy classes — view the full character table.
| maximal subgroup of | Dic211⋊C25, C4×C211⋊C25, C2×D211⋊C25, … |
| maximal normal subgroup of | Dic211⋊C25, C4×C211⋊C25, C2×D211⋊C25, … |
| maximal quotient of | C4×C211⋊C25, C22×C211⋊C25, C2×C3×C211⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10550, 3);