Finite Group DatabasebetaFinite Group Databasebeta| order | 31964 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C131⋊#6923 |
| Fitting, socle, derived, Hall | C61×C131 ⋊ C4 |
| Sylow | C131 ⋊ #6923 |
| Sylow | C61 ⋊ Dic131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C61×C131 | C4 |
| prime radical, cosocle | D61×C131 | C2 |
| LCS | G ▷ C61×C131 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7991 |
Polycyclic presentation:
2^2,61,131|a^2=b,c^a=c^50,d^a=d^130,c^b=c^602099 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31964, 7);