Finite Group DatabasebetaFinite Group Databasebeta| order | 32079 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C37⋊(C172⋊C3) |
| unambiguous semidirect product | C172⋊(C37⋊C3) |
| Fitting, socle, derived, Hall | C172×C37 ⋊ C3 |
| Sylow | C172 ⋊ C37⋊C3 |
| Sylow | C37 ⋊ C172⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C172×C37 | C3 |
| LCS | G ▷ C172×C37 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1887 |
Polycyclic presentation:
3,17^2,37|b^a=b^2c^15,c^a=b^12c^14,d^a=d^263567 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32079, 5);