Finite Group DatabasebetaFinite Group Databasebeta| order | 12069 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 575424 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C9 |
| abelian | C92×C149 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32 | C32×C149 |
| socle, prime radical | C32×C149 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
46 conjugacy classes of subgroups.
12069 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C27×C149, C149×#6864, C149×C9⋊C27, … |
| maximal normal subgroup of | C9×C27×C149, C149×#6864, C149×C9⋊C27, … |
| maximal quotient of | C149×#6855, C9×C27×C149, C149×#6864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12069, 2);