Finite Group DatabasebetaFinite Group Databasebeta| order | 31620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D3×C31×D85 |
| unambiguous semidirect product | (C5×D3)⋊(C31×D17) |
| unambiguous semidirect product | (D3×C17)⋊(D5×C31) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D3×D85 |
| commutator, cosocle, hypocenter | C3×C5×C17 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C17×C31 | C22 |
| LCS | G ▷ C3×C5×C17 | |
| UCS | C1 ◁ C31 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7905 |
4092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31620, 143);