Finite Group DatabasebetaFinite Group Databasebeta| order | 32079 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C289 · Schur multiplier (H2) = C1 |
| direct product | C37⋊C3×C289 |
| unambiguous semidirect product | C37⋊(C3×C289) |
| unambiguous semidirect product | (C37×C289)⋊C3 |
| Fitting, Hall | C37×C289 ⋊ C3 |
| derived, Sylow | C37 ⋊ C3×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | C37⋊C3 |
| commutator, hypocenter | C37 | C3×C289 |
| Frattini | C17 | C17×C37⋊C3 |
| Fitting | C37×C289 | C3 |
| socle, cosocle | C17×C37 | C3×C17 |
| prime radical | C17×C37⋊C3 | C17 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C289 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10693 |
4335 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32079, 2);