Finite Group DatabasebetaFinite Group Databasebeta| order | 15996 |
| isoclinism | isoclinic class of C22⋊(C31⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C43 · Schur multiplier (H2) = C2 |
| direct product | C43×C22⋊(C31⋊C3) |
| unambiguous semidirect product | C22⋊(C43×C31⋊C3) |
| unambiguous semidirect product | C31⋊(A4×C43) |
| Fitting, socle, Hall | C22×C31×C43 ⋊ C3 |
| derived, Hall | C22×C31 ⋊ C3×C43 |
| Hall | C31×C43 ⋊ A4 |
| Hall | C22×C43 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ A4×C43 |
| Sylow | C22 ⋊ C43×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C22⋊(C31⋊C3) |
| commutator, cosocle, hypocenter | C22×C31 | C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C22×C31×C43 | C3 |
| LCS | G ▷ C22×C31 | |
| UCS | C1 ◁ C43 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5332 |
1892 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15996, 51);