Finite Group DatabasebetaFinite Group Databasebeta| order | 32786 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C97 · Schur multiplier (H2) = C1 |
| direct product | C97×D169 |
| unambiguous semidirect product | C169⋊(C2×C97) |
| Fitting, Hall | C97×C169 ⋊ C2 |
| derived, Sylow | C169 ⋊ C2×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | D169 |
| commutator, cosocle, hypocenter | C169 | C2×C97 |
| Frattini | C13 | D13×C97 |
| Fitting | C97×C169 | C2 |
| socle | C13×C97 | D13 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C97 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16393 |
8342 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32786, 2);