Finite Group DatabasebetaFinite Group Databasebeta| order | 31980 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (Dic533⋊C3)⋊C5 |
| unambiguous semidirect product | (Dic533⋊C5)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C13⋊C3)⋊(D41⋊C5) |
| commutator, hypocenter | C13×C41 | C3×C4×C5 |
| Fitting, socle, cosocle | C2×C13×C41 | C2×C3×C5 |
| prime radical | C2×C13⋊C3×C41⋊C5 | C2 |
| LCS | G ▷ C13×C41 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2132 |
Polycyclic presentation:
2,3,5,13,41,2|a^2=f,d^a=d^12,e^a=e^40,d^b=d^3,e^c=e^10136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31980, 36);