Finite Group DatabasebetaFinite Group Databasebeta| order | 31236 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊#10587739 |
| unambiguous semidirect product | (C19⋊#10587739)⋊C3 |
| Fitting, socle, derived, Hall | C19×C137 ⋊ C3×C4 |
| Hall | C19⋊#10587739 ⋊ C3 |
| Hall | C19⋊C3×C137 ⋊ C4 |
| Sylow | C137 ⋊ (C19⋊C3)⋊C4 |
| Hall | C19⋊C3 ⋊ #10587739 |
| Sylow | C19 ⋊ C3×#10587739 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C137 | C3×C4 |
| prime radical | C19⋊C3×D137 | C2 |
| cosocle | C19×D137 | C2×C3 |
| LCS | G ▷ C19×C137 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2603 |
Polycyclic presentation:
2,3,2,19,137|a^2=c,d^a=d^18,e^a=e^100,d^b=d^7,e^c=e^136324 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31236, 14);