Finite Group DatabasebetaFinite Group Databasebeta| order | 32705 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C211 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽32)×C211 |
| unambiguous semidirect product | C31⋊(C5×C211) |
| Fitting, socle, Hall | C31×C211 ⋊ C5 |
| derived, Sylow | C31 ⋊ C5×C211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C211 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C5×C211 |
| Frattini | C1 | G |
| Fitting, socle | C31×C211 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C211 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6541 |
2321 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32705, 1);