Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AΣL(1,𝔽27) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C37 · Schur multiplier (H2) = C34 |
| direct product | C3×C37×#732 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C37 | H(3,𝔽3) |
| commutator, Frattini | C32 | C33×C37 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C37 ◁ C33×C37 ◁ G | |
168 conjugacy classes of subgroups.
1887 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 53);