Finite Group DatabasebetaFinite Group Databasebeta| order | 10285 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#10597244 |
| Fitting, socle, Hall | C112×C17 ⋊ C5 |
| derived, Sylow | C112 ⋊ C5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #10597244 |
| commutator, cosocle, hypocenter | C112 | C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C112×C17 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C17 | |
20 conjugacy classes of subgroups.
493 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#10597244, C17×#11925898, C17⋊#11925898, … |
| maximal normal subgroup of | D17×#10597244, C17×#11925898, C17⋊#11925898, … |
| maximal quotient of | C2×C17×#10597244, C3×C17×#10597244 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10285, 6);