Finite Group DatabasebetaFinite Group Databasebeta| order | 10550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×D211⋊C5 |
| unambiguous semidirect product | D211⋊C52 |
| unambiguous semidirect product | (C211⋊C5)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D211)⋊C5 |
| Fitting, socle | C5×C211 ⋊ C2×C5 |
| derived, Sylow | C211 ⋊ C2×C52 |
| Hall | C5×C211⋊C5 ⋊ C2 |
| Hall | D211 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D211⋊C5 |
| commutator, cosocle, hypocenter | C211 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C211 | C2×C5 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
155 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D211⋊C5, C2×C5×D211⋊C5, C5×(D211⋊C3)⋊C5, … |
| maximal normal subgroup of | D5×D211⋊C5, C2×C5×D211⋊C5, C5×(D211⋊C3)⋊C5, … |
| maximal quotient of | C5×Dic211⋊C5, C2×C5×D211⋊C5, C3×C5×D211⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10550, 8);