Finite Group DatabasebetaFinite Group Databasebeta| order | 8649 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C961⋊C9 |
| derived, Sylow | C961 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C961⋊C3 |
| commutator, hypocenter | C961 | C9 |
| Frattini, socle | C3×C31 | C31⋊C3 |
| Fitting | C3×C961 | C3 |
| LCS | G ▷ C961 | |
| UCS | C1 ◁ C3 | |
9 conjugacy classes of subgroups.
Polycyclic presentation:
3,31,3,31|a^3=c,b^31=d^2,b^a=b^25d,d^a=d^25969 conjugacy classes — view the full character table.
| maximal subgroup of | D961⋊C9, C2×C961⋊C9, C22⋊(C961⋊C9) |
| maximal normal subgroup of | D961⋊C9, C2×C961⋊C9 |
| maximal quotient of | C2×C961⋊C9, C22⋊(C961⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8649, 2);