Finite Group DatabasebetaFinite Group Databasebeta| order | 32037 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×C181⋊C3 |
| unambiguous semidirect product | C181⋊(C3×C59) |
| unambiguous semidirect product | (C59×C181)⋊C3 |
| Fitting, socle, Hall | C59×C181 ⋊ C3 |
| derived, Sylow | C181 ⋊ C3×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | C181⋊C3 |
| commutator, cosocle, hypocenter | C181 | C3×C59 |
| Frattini | C1 | G |
| Fitting, socle | C59×C181 | C3 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C59 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10679 |
3717 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32037, 1);