Finite Group DatabasebetaFinite Group Databasebeta| order | 10287 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C9 |
| direct product | C9×#11765919 |
| Fitting | C9×C127 ⋊ C9 |
| derived, Sylow | C127 ⋊ C92 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #11765919 |
| commutator, hypocenter | C127 | C92 |
| Frattini | C3 | C3×#11765919 |
| Fitting | C9×C127 | C9 |
| socle | C3×C127 | C3×C9 |
| prime radical, cosocle | C3×C127⋊C3 | C32 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C9 | |
46 conjugacy classes of subgroups.
207 conjugacy classes — view the full character table.
| maximal subgroup of | C27×#11765919, #44525160, #44525161, … |
| maximal normal subgroup of | C27×#11765919, #44525160, #44525161, … |
| maximal quotient of | (C3×#11765919)⋊C9, C27×#11765919, C9×#16812186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10287, 51);