Finite Group DatabasebetaFinite Group Databasebeta| order | 31122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D819 |
| unambiguous semidirect product | C7⋊(C19×D117) |
| unambiguous semidirect product | C9⋊(C19×D91) |
| unambiguous semidirect product | C13⋊(C19×D63) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D819 |
| commutator, cosocle, hypocenter | C7×C9×C13 | C2×C19 |
| Frattini | C3 | C19×D273 |
| Fitting | C7×C9×C13×C19 | C2 |
| socle | C3×C7×C13×C19 | D3 |
| LCS | G ▷ C7×C9×C13 | |
| UCS | C1 ◁ C19 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15561 |
7809 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31122, 28);