Finite Group DatabasebetaFinite Group Databasebeta| order | 8019 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C9×C11 · Schur multiplier (H2) = C35 |
| direct product | C32×C11×C27⋊C3 |
| unambiguous semidirect product | C27⋊(C33×C11) |
| unambiguous semidirect product | (C11×C27)⋊C33 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C9×C11 | C32 |
| commutator | C3 | C33×C9×C11 |
| Frattini | C9 | C34×C11 |
| socle | C33×C11 | C3×C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C9×C11 ◁ G | |
944 conjugacy classes of subgroups.
3267 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8019, 476);