Finite Group DatabasebetaFinite Group Databasebeta| order | 31122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | AGL(1,𝔽7)×#10625203 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C2×#10625203) |
| 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 |
595 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31122, 182);