Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #14546369 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3 | #10624474 |
| commutator, Frattini, cosocle | C32×H(3,𝔽3) | C32 |
| prime radical | #10624754 | C3 |
| LCS | G ▷ C32×H(3,𝔽3) ▷ C34 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3 ◁ C32 ◁ C34 ◁ C32×H(3,𝔽3) ◁ G | |
| LECS | G ▷ C32×H(3,𝔽3) ▷ C34 ▷ C32 ▷ C3 ▷ C1 | |
173 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
3^7|b^3=g,b^a=bc,c^a=cd,d^a=dg^2,e^a=efg,f^a=fg,c^b=ce,d^b=df,d^c=dg59 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 229);