Finite Group DatabasebetaFinite Group Databasebeta| order | 3897 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C433 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C433⋊C3 |
| commutator, hypocenter | C433 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C433 | C3 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 442 |
| transitive degree | μt(G) = 3897 |
Polycyclic presentation:
3^2,433|a^3=b,c^a=c^198441 conjugacy classes — view the full character table.
| maximal subgroup of | C9×C433⋊C3, C3×#16838985, #26043125, … |
| maximal normal subgroup of | C9×C433⋊C3, C3×#16838985, #26043125, … |
| maximal quotient of | #26043121, C3×#16838985, C22⋊#16838985, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3897, 1);