Finite Group DatabasebetaFinite Group Databasebeta| order | 20667 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C83 |
| unambiguous semidirect product | C832⋊C3 |
| Fitting, socle, derived, Sylow | C832 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C832 | C3 |
| LCS | G ▷ C832 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 249 |
Polycyclic presentation:
3,83^2|b^a=b^44c^77,c^a=b^12c^382299 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20667, 2);