Finite Group DatabasebetaFinite Group Databasebeta| order | 31620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽32)⋊Dic17) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊Dic51 |
| unambiguous semidirect product | Dic1581⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C17⋊(D31⋊C5)) |
| commutator, hypocenter | C3×C17×C31 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C17×C31 | C2×C5 |
| prime radical | C2×C3×C17×ΓL(1,𝔽32) | C2 |
| LCS | G ▷ C3×C17×C31 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6324 |
Polycyclic presentation:
2,3,5,17,31,2|a^2=f,b^a=b^2,d^a=d^16,e^a=e^30,e^c=e^16576 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31620, 26);