Finite Group DatabasebetaFinite Group Databasebeta| order | 31236 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊Dic137 |
| unambiguous semidirect product | Dic2603⋊C3 |
| derived, Hall | C19×C137 ⋊ C3×C4 |
| Hall | Dic2603 ⋊ C3 |
| Hall | C19⋊C3×C137 ⋊ C4 |
| Sylow | C137 ⋊ (C19⋊C3)⋊C4 |
| Hall | C19⋊C3 ⋊ Dic137 |
| Sylow | C19 ⋊ C3×Dic137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C19⋊C3)⋊D137 |
| commutator, hypocenter | C19×C137 | C3×C4 |
| Fitting, socle, cosocle | C2×C19×C137 | C2×C3 |
| prime radical | C2×C19⋊C3×C137 | C2 |
| LCS | G ▷ C19×C137 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10412 |
Polycyclic presentation:
2,3,19,137,2|a^2=e,c^a=c^18,d^a=d^136,c^b=c^71242 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31236, 12);