Finite Group DatabasebetaFinite Group Databasebeta| order | 31980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic533⋊C5) |
| unambiguous semidirect product | Dic1599⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C13⋊(D41⋊C5)) |
| commutator, hypocenter | C3×C13×C41 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C13×C41 | C2×C5 |
| prime radical | C2×C3×C13×C41⋊C5 | C2 |
| LCS | G ▷ C3×C13×C41 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6396 |
Polycyclic presentation:
2,3,5,13,41,2|a^2=f,b^a=b^2,d^a=d^12,e^a=e^40,e^c=e^10522 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31980, 26);