Finite Group DatabasebetaFinite Group Databasebeta| order | 19629 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C727 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C727⋊C3 |
| commutator, socle, cosocle | C3×C727 | C32 |
| Fitting, prime radical | C32×C727 | C3 |
| hypercenter | C32 | C727⋊C3 |
| hypocenter | C727 | 3−1+2 |
| LCS | G ▷ C3×C727 ▷ C727 | |
| UCS | C1 ◁ C3 ◁ C32 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6543 |
Polycyclic presentation:
3^3,727|a^3=c,b^a=bc,d^a=d^4452189 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19629, 12);