Finite Group DatabasebetaFinite Group Databasebeta| order | 10611 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 42120 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3 |
| abelian | C3×C27×C131 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C9 | C32×C131 |
| socle, prime radical | C32×C131 | C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
28 conjugacy classes of subgroups.
10611 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C27×C131, C131×#6864, C131×C32⋊C27, … |
| maximal normal subgroup of | C9×C27×C131, C131×#6864, C131×C32⋊C27, … |
| maximal quotient of | C9×C27×C131, C131×C32⋊C27, C131×C9⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10611, 5);