Finite Group DatabasebetaFinite Group Databasebeta| order | 31980 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×#11717961 |
| unambiguous semidirect product | (C13×#11717961)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C41 | C3×C4 |
| prime radical | C13⋊C3×D205 | C2 |
| cosocle | C13×D205 | C2×C3 |
| LCS | G ▷ C5×C13×C41 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2665 |
385 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31980, 90);