Finite Group DatabasebetaFinite Group Databasebeta| order | 10719 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C397 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C397⋊C3 |
| commutator, socle, cosocle | C3×C397 | C32 |
| Fitting, prime radical | C32×C397 | C3 |
| hypercenter | C32 | C397⋊C3 |
| hypocenter | C397 | 3−1+2 |
| LCS | G ▷ C3×C397 ▷ C397 | |
| UCS | C1 ◁ C3 ◁ C32 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,397|a^3=c,b^a=bc,d^a=d^3621199 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44565431, #44565432, #44565433, … |
| maximal normal subgroup of | #44565431, #44565432, #44565433, … |
| maximal quotient of | C32⋊#16813208, #44565423, C3×#24924308 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10719, 12);