Finite Group DatabasebetaFinite Group Databasebeta| order | 1323 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C9⋊#3862 |
| Fitting | C72×C9 ⋊ C3 |
| Sylow | C72 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×#3862 |
| commutator, socle, cosocle | C3×C72 | C32 |
| Fitting | C72×C9 | C3 |
| prime radical | C3×#3862 | C3 |
| hypercenter | C9 | #3862 |
| hypocenter | C72 | 3−1+2 |
| LCS | G ▷ C3×C72 ▷ C72 | |
| UCS | C1 ◁ C3 ◁ C9 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
Polycyclic presentation:
3^3,7^2|b^3=c,b^a=bc,d^a=d^4,e^a=e^2155 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1323, 40);