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 | C3 | #16813210 |
| commutator, hypocenter | C397 | C27 |
| Fitting, socle, prime radical | C3×C397 | C9 |
| cosocle | #16813208 | C3 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,397|a^3=b,b^3=c,d^a=d^79,d^b=d^362159 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#24924310, (C397⋊C3)⋊C27, #44565460, … |
| maximal normal subgroup of | C3×#24924310, (C397⋊C3)⋊C27, #44565460, … |
| maximal quotient of | #44565453, C3×#24924310 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10719, 14);