Finite Group DatabasebetaFinite Group Databasebeta| order | 1323 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)2 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #3862⋊C9 |
| derived, Sylow | C72 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)2 |
| commutator, hypocenter | C72 | C3×C9 |
| Fitting, socle, cosocle | C3×C72 | C32 |
| prime radical | C3×#3862 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
Polycyclic presentation:
3^3,7^2|a^3=c,b^3=c,e^a=e^2,d^b=d^275 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1323, 19);