Finite Group DatabasebetaFinite Group Databasebeta| order | 31980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D39⋊D41 |
| unambiguous semidirect product | D39⋊(C5×D41) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D39⋊D41 |
| commutator, cosocle, hypocenter | C3×C13×C41 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13×C41 | C22 |
| LCS | G ▷ C3×C13×C41 | |
| UCS | C1 ◁ C5 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7995 |
2220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31980, 166);