Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6875 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C81 · Schur multiplier (H2) = C3 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center | C3×C9 | C9⋊C9 |
| commutator | C9 | C3×C81 |
| Frattini, cosocle | C9×C27 | C32 |
| socle, prime radical | C32 | C9⋊C27 |
| LCS | G ▷ C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9 ◁ C9×C27 ◁ G | |
| LECS | G ▷ C9×C27 ▷ C3×C9 ▷ C3 ▷ C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2187 |
Polycyclic presentation:
3^7|a^3=d,b^3=c,c^3=e,d^3=f,f^3=g,b^a=bc,c^a=ce,d^b=de^2315 conjugacy classes — view the full character table.
| Fitting subgroup of | #72277428 |
| maximal subgroup of | #72277428, #72277430 |
| maximal normal subgroup of | #72277428, #72277430 |
| maximal quotient of | #72277430, #72277453 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 193);