Finite Group DatabasebetaFinite Group Databasebeta| order | 31122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D19×#11717941 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D19×#63270 |
| commutator, hypocenter | C7×C13×C19 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C13×C19 | C2×C3 |
| prime radical | C3×C7×C13×D19 | C3 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15561 |
1089 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31122, 37);