Finite Group DatabasebetaFinite Group Databasebeta| order | 1323 |
| isoclinism | isoclinic class of C49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×C49⋊C9 |
| unambiguous semidirect product | (C3×C49)⋊C9 |
| derived, Sylow | C49 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C49⋊C3 |
| commutator, hypocenter | C49 | C3×C9 |
| Frattini | C3×C7 | C3×ΓL(1,𝔽8) |
| Fitting | C32×C49 | C3 |
| socle, prime radical | C32×C7 | ΓL(1,𝔽8) |
| cosocle | C3×C49 | C32 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C32 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1323 |
171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1323, 6);