Finite Group DatabasebetaFinite Group Databasebeta| order | 15996 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C31 · Schur multiplier (H2) = C2 |
| direct product | C31×C22⋊(C43⋊C3) |
| unambiguous semidirect product | C22⋊(C31×C43⋊C3) |
| unambiguous semidirect product | C43⋊(A4×C31) |
| Fitting, socle, Hall | C22×C31×C43 ⋊ C3 |
| derived, Hall | C22×C43 ⋊ C3×C31 |
| Hall | C31×C43 ⋊ A4 |
| Hall | C22×C31 ⋊ C43⋊C3 |
| Sylow | C43 ⋊ A4×C31 |
| Sylow | C22 ⋊ C31×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C22⋊(C43⋊C3) |
| commutator, cosocle, hypocenter | C22×C43 | C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C22×C31×C43 | C3 |
| LCS | G ▷ C22×C43 | |
| UCS | C1 ◁ C31 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5332 |
1860 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15996, 52);