Finite Group DatabasebetaFinite Group Databasebeta| order | 10285 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C121⋊C5 |
| unambiguous semidirect product | C121⋊(C5×C17) |
| unambiguous semidirect product | (C17×C121)⋊C5 |
| Fitting, Hall | C17×C121 ⋊ C5 |
| derived, Sylow | C121 ⋊ C5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C121⋊C5 |
| commutator, cosocle, hypocenter | C121 | C5×C17 |
| Frattini | C11 | C17×C11⋊C5 |
| Fitting | C17×C121 | C5 |
| socle | C11×C17 | C11⋊C5 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C17 | |
12 conjugacy classes of subgroups.
493 conjugacy classes — view the full character table.
| maximal subgroup of | D17×C121⋊C5, C17×D121⋊C5, C17⋊(D121⋊C5), … |
| maximal normal subgroup of | D17×C121⋊C5, C17×D121⋊C5, C17⋊(D121⋊C5), … |
| maximal quotient of | C2×C17×C121⋊C5, C3×C17×C121⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10285, 2);