Finite Group DatabasebetaFinite Group Databasebeta| order | 32798 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D529 |
| unambiguous semidirect product | C529⋊(C2×C31) |
| Fitting, Hall | C31×C529 ⋊ C2 |
| derived, Sylow | C529 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D529 |
| commutator, cosocle, hypocenter | C529 | C2×C31 |
| Frattini | C23 | C31×D23 |
| Fitting | C31×C529 | C2 |
| socle | C23×C31 | D23 |
| LCS | G ▷ C529 | |
| UCS | C1 ◁ C31 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16399 |
8246 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32798, 2);