Finite Group DatabasebetaFinite Group Databasebeta| order | 8829 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C109 · Schur multiplier (H2) = C1 |
| direct product | C27⋊C3×C109 |
| unambiguous semidirect product | C27⋊(C3×C109) |
| subgroup | G/H | |
|---|---|---|
| center | C9×C109 | C32 |
| commutator | C3 | C3×C9×C109 |
| Frattini | C9 | C32×C109 |
| socle | C3×C109 | C3×C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9×C109 ◁ G | |
24 conjugacy classes of subgroups.
3597 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8829, 6);