Finite Group DatabasebetaFinite Group Databasebeta| order | 31122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊#13093361 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C19 | C2×C32 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1729 |
Polycyclic presentation:
2,3^2,7,13,19|d^a=d^6,f^a=f^18,e^b=e^3,f^b=f^11,d^c=d^2244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31122, 174);