Finite Group DatabasebetaFinite Group Databasebeta| order | 10719 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C9×C397 ⋊ C3 |
| Sylow | C397 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C397⋊C3 |
| commutator, socle, cosocle | C3×C397 | C32 |
| Fitting | C9×C397 | C3 |
| prime radical | C3×C397⋊C3 | C3 |
| hypercenter | C9 | C397⋊C3 |
| hypocenter | C397 | 3−1+2 |
| LCS | G ▷ C3×C397 ▷ C397 | |
| UCS | C1 ◁ C3 ◁ C9 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,397|a^3=c,b^a=bc,d^b=d^3621199 conjugacy classes. The character table is too large to display.
| maximal subgroup of | 3−1+2×C397⋊C3, C3×#24924306, #44565450, … |
| maximal normal subgroup of | 3−1+2×C397⋊C3, C3×#24924306, #44565450, … |
| maximal quotient of | #44565421, #44565423, #44565425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10719, 10);