Finite Group DatabasebetaFinite Group Databasebeta| order | 10287 |
| automorphism | ? |
| homology | Abelianization (H1) = C81 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C127 ⋊ C81 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | #11765919 |
| commutator, hypocenter | C127 | C81 |
| Fitting | C9×C127 | C9 |
| socle, prime radical | C3×C127 | C27 |
| cosocle | #16812178 | C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C9 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,127|a^3=b,b^3=c,c^3=d,e^a=e^22,e^b=e^107207 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#23779863, (C127⋊C3)⋊C81, #44525189, … |
| maximal normal subgroup of | C3×#23779863, (C127⋊C3)⋊C81, #44525189, … |
| maximal quotient of | #44525156, C3×#23779863 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10287, 50);