Finite Group DatabasebetaFinite Group Databasebeta| order | 10719 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C397 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | C397⋊C3 |
| commutator, hypocenter | C397 | C27 |
| Fitting, cosocle | C9×C397 | C3 |
| socle, prime radical | C3×C397 | C9 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C9 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,397|a^3=b,b^3=c,d^a=d^3621215 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C27×C397⋊C3, C3×#24924302, #44565428, … |
| maximal normal subgroup of | C27×C397⋊C3, C3×#24924302, #44565428, … |
| maximal quotient of | #44565419, C3×#24924302 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10719, 6);