Finite Group DatabasebetaFinite Group Databasebeta| order | 15996 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C43⋊C3)⋊Dic31 |
| derived, Hall | C31×C43 ⋊ C3×C4 |
| Hall | Dic1333 ⋊ C3 |
| Hall | C31×C43⋊C3 ⋊ C4 |
| Hall | C43⋊C3 ⋊ Dic31 |
| Sylow | C43 ⋊ C3×Dic31 |
| Sylow | C31 ⋊ (C43⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C43⋊C3)⋊D31 |
| commutator, hypocenter | C31×C43 | C3×C4 |
| Fitting, socle, cosocle | C2×C31×C43 | C2×C3 |
| prime radical | C2×C31×C43⋊C3 | C2 |
| LCS | G ▷ C31×C43 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5332 |
Polycyclic presentation:
2,3,31,43,2|a^2=e,c^a=c^30,d^a=d^42,d^b=d^36536 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15996, 21);