Finite Group DatabasebetaFinite Group Databasebeta| order | 31122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3 |
| direct product | C3×C13×ΓL(1,𝔽8)⋊D19 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C3×C13×D19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | ΓL(1,𝔽8)⋊D19 |
| commutator, cosocle, hypocenter | C7×C19 | C2×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C19 | C2×C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C3×C13 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5187 |
2028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31122, 315);