Finite Group DatabasebetaFinite Group Databasebeta| order | 31122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#17984640 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #17984640 |
| commutator, hypocenter | C13×C19 | C2×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C19 | C2×C9 |
| prime radical | C7×D13×C19⋊C3 | C3 |
| cosocle | C13×C19⋊C3 | C2×C3×C7 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C7 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1729 |
280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31122, 125);