Finite Group DatabasebetaFinite Group Databasebeta| order | 1323 |
| isoclinism | isoclinic class of C49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C32×C49⋊C3 |
| unambiguous semidirect product | C49⋊C33 |
| unambiguous semidirect product | (C3×C49)⋊C32 |
| Fitting | C32×C49 ⋊ C3 |
| derived, Sylow | C49 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C33 |
| Frattini | C7 | C32×ΓL(1,𝔽8) |
| Fitting | C32×C49 | C3 |
| socle | C32×C7 | ΓL(1,𝔽8) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C32 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 441 |
171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1323, 16);