Finite Group DatabasebetaFinite Group Databasebeta| order | 10719 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C397 · Schur multiplier (H2) = C32 |
| direct product | H(3,𝔽3)×C397 |
| unambiguous semidirect product | C32⋊(C3×C397) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C397 | C32 |
| commutator, Frattini, cosocle | C3 | C32×C397 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C397 ◁ G | |
22 conjugacy classes of subgroups.
4367 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10719, 3);