Finite Group DatabasebetaFinite Group Databasebeta| order | 10791 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#11758281 |
| Fitting, socle, Hall | C11×C109 ⋊ C9 |
| derived, Sylow | C109 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #11758281 |
| commutator, hypocenter | C109 | C9×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C109 | C9 |
| prime radical | C11×C109⋊C3 | C3 |
| cosocle | C109⋊C3 | C3×C11 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C11 | |
12 conjugacy classes of subgroups.
231 conjugacy classes — view the full character table.
| maximal subgroup of | C11×#11758281⋊C2, C11⋊(#11758281⋊C2), D11×#11758281, … |
| maximal normal subgroup of | C11×#11758281⋊C2, C11⋊(#11758281⋊C2), D11×#11758281, … |
| maximal quotient of | C2×C11×#11758281 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10791, 4);