Finite Group DatabasebetaFinite Group Databasebeta| order | 7047 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9×C29 · Schur multiplier (H2) = C33 |
| direct product | C3×C29×C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C29 | C32 |
| commutator | C3 | C32×C9×C29 |
| Frattini | C32 | C33×C29 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C33×C29 ◁ G | |
180 conjugacy classes of subgroups.
2871 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7047, 33);