Finite Group DatabasebetaFinite Group Databasebeta| order | 10287 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C127⋊C3)⋊C27 |
| derived, Sylow | C127 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #11765919 |
| commutator, hypocenter | C127 | C3×C27 |
| Frattini | C3 | C3×#11765919 |
| Fitting | C9×C127 | C9 |
| socle | C3×C127 | C3×C9 |
| prime radical | C3×C127⋊C3 | C9 |
| cosocle | #11765917 | C32 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C9 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,127|a^3=c,c^3=d,e^a=e^22,e^b=e^19,e^c=e^107207 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 | C9×#16812186, #44525164, #44525179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10287, 56);