Finite Group DatabasebetaFinite Group Databasebeta| order | 31707 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C271 ⋊ C9 |
| Sylow | C271 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ #14578514 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C271 | C9 |
| prime radical, cosocle | C13×C271⋊C3 | C3 |
| LCS | G ▷ C13×C271 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3523 |
Polycyclic presentation:
3^2,13,271|a^3=b,c^a=c^3,d^a=d^169,d^b=d^28411 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31707, 8);