Finite Group DatabasebetaFinite Group Databasebeta| order | 10284 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#16812170 |
| Fitting, socle, Hall | C3×C857 ⋊ C4 |
| derived, Sylow | C857 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16812170 |
| commutator, hypocenter | C857 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C857 | C4 |
| prime radical | C3×D857 | C2 |
| cosocle | D857 | C2×C3 |
| LCS | G ▷ C857 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
654 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#16812170, C32×#16812170, C3×C3⋊#16812170 |
| maximal normal subgroup of | C9×#16812170, C32×#16812170 |
| maximal quotient of | C9×#16812170, C32×#16812170, C3×C3⋊#16812170 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10284, 6);