Finite Group DatabasebetaFinite Group Databasebeta| order | 31692 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C139 · Schur multiplier (H2) = C2 |
| direct product | C139×C22⋊(C19⋊C3) |
| unambiguous semidirect product | C22⋊(C19⋊C3×C139) |
| unambiguous semidirect product | C19⋊(A4×C139) |
| Fitting, socle, Hall | C22×C19×C139 ⋊ C3 |
| derived, Hall | C22×C19 ⋊ C3×C139 |
| Hall | C19×C139 ⋊ A4 |
| Hall | C22×C139 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ A4×C139 |
| Sylow | C22 ⋊ C19⋊C3×C139 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C139 | C22⋊(C19⋊C3) |
| commutator, cosocle, hypocenter | C22×C19 | C3×C139 |
| Frattini | C1 | G |
| Fitting, socle | C22×C19×C139 | C3 |
| LCS | G ▷ C22×C19 | |
| UCS | C1 ◁ C139 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10564 |
3892 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31692, 51);