Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #10624477 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C3×#10624479 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32 | #6856 |
| commutator, Frattini, cosocle | C32×C9 | C33 |
| prime radical | C34 | H(3,𝔽3) |
| LCS | G ▷ C32×C9 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32 ◁ C34 ◁ C33×C9 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C33 ▷ C3 ▷ C1 | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 84 |
| transitive degree | μt(G) = 243 |
123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 4682);