Finite Group DatabasebetaFinite Group Databasebeta| order | 31980 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×Dic205 |
| unambiguous semidirect product | (C13×Dic205)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C13⋊C3×D205 |
| commutator, hypocenter | C5×C13×C41 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C13×C41 | C2×C3 |
| prime radical | C2×C5×C13⋊C3×C41 | C2 |
| LCS | G ▷ C5×C13×C41 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10660 |
1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31980, 31);