Finite Group DatabasebetaFinite Group Databasebeta| order | 10611 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C131 · Schur multiplier (H2) = C1 |
| direct product | C27⋊C3×C131 |
| unambiguous semidirect product | C27⋊(C3×C131) |
| unambiguous semidirect product | (C27×C131)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center | C9×C131 | C32 |
| commutator | C3 | C3×C9×C131 |
| Frattini, cosocle | C9 | C32×C131 |
| socle | C3×C131 | C3×C9 |
| prime radical | C32×C131 | C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9×C131 ◁ G | |
24 conjugacy classes of subgroups.
4323 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C131×#6869, C131×#6872, C131×#6873, … |
| maximal normal subgroup of | C131×#6869, C131×#6872, C131×#6873, … |
| maximal quotient of | C131×#6864, C131×C32⋊C27, C131×C9⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10611, 6);