Finite Group DatabasebetaFinite Group Databasebeta| order | 10287 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C32×#11765917 |
| derived, Sylow | C127 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | C127⋊C3 |
| commutator, hypocenter | C127 | C32×C9 |
| Frattini | C3 | C32×C127⋊C3 |
| Fitting, socle, prime radical | C33×C127 | C3 |
| cosocle | C3×C127 | C33 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C33 | |
100 conjugacy classes of subgroups.
1215 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44524915, #44524943, #44524945, … |
| maximal normal subgroup of | #44524915, #44524943, #44524945, … |
| maximal quotient of | C3×C9×#11765917, C3×C32⋊#11765917, C3×#23779834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10287, 39);