Finite Group DatabasebetaFinite Group Databasebeta| order | 10535 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C49 · Schur multiplier (H2) = C1 |
| direct product | C5×C43⋊C49 |
| unambiguous semidirect product | C43⋊(C5×C49) |
| unambiguous semidirect product | (C5×C43)⋊C49 |
| derived, Sylow | C43 ⋊ C5×C49 |
| Hall | C5×C43 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | C43⋊C7 |
| commutator, hypocenter | C43 | C5×C49 |
| Frattini | C7 | C5×C43⋊C7 |
| Fitting, socle, prime radical | C5×C7×C43 | C7 |
| cosocle | C7×C43 | C5×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C5×C7 | |
12 conjugacy classes of subgroups.
455 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×C43⋊C49, C5×D43⋊C49, D5×C43⋊C49, … |
| maximal normal subgroup of | C2×C5×C43⋊C49, C5×D43⋊C49, D5×C43⋊C49, … |
| maximal quotient of | C2×C5×C43⋊C49, C3×C5×C43⋊C49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10535, 2);