Finite Group DatabasebetaFinite Group Databasebeta| order | 31236 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19×C137 · Schur multiplier (H2) = C2 |
| direct product | A4×C19×C137 |
| unambiguous semidirect product | C22⋊(C3×C19×C137) |
| unambiguous semidirect product | (C22×C137)⋊(C3×C19) |
| Fitting, socle, Hall | C22×C19×C137 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C19×C137 |
| Hall | C22×C137 ⋊ C3×C19 |
| Hall | C22×C19 ⋊ C3×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19×C137 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C19×C137 |
| Frattini | C1 | G |
| Fitting, socle | C22×C19×C137 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C19×C137 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10412 |
10412 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31236, 31);