Finite Group DatabasebetaFinite Group Databasebeta| order | 31236 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C3×C19×#10587739 |
| Fitting, socle, Hall | C3×C19×C137 ⋊ C4 |
| derived, Sylow | C137 ⋊ C3×C4×C19 |
| Hall | C19×C137 ⋊ C3×C4 |
| Hall | C3×C137 ⋊ C4×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | #10587739 |
| commutator, hypocenter | C137 | C3×C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C137 | C4 |
| prime radical | C3×C19×D137 | C2 |
| cosocle | D137 | C2×C3×C19 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C3×C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7809 |
2166 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31236, 20);