Finite Group DatabasebetaFinite Group Databasebeta| order | 31620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽32)⋊#595) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C3⋊#595) |
| unambiguous semidirect product | (C3⋊(C31⋊#595))⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C17×C31 | C4×C5 |
| prime radical | C3×D17×ΓL(1,𝔽32) | C2 |
| cosocle | C3×C31×D17 | C2×C5 |
| LCS | G ▷ C3×C17×C31 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1581 |
Polycyclic presentation:
2,5,2,3,17,31|a^2=c,d^a=d^2,e^a=e^13,f^a=f^30,f^b=f^16,e^c=e^16180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31620, 48);