Finite Group DatabasebetaFinite Group Databasebeta| order | 31620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽32)×C3⋊#595 |
| unambiguous semidirect product | C3⋊(#595×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C31×C3⋊#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 |
198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31620, 49);