Finite Group DatabasebetaFinite Group Databasebeta| order | 20439 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C757 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C757 | C27 |
| prime radical | C757⋊C3 | C9 |
| cosocle | #20291842 | C3 |
| LCS | G ▷ C757 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 757 |
Polycyclic presentation:
3^3,757|a^3=b,b^3=c,d^a=d^228,d^b=d^3,d^c=d^2755 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20439, 16);