Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C92 · Schur multiplier (H2) = C32×C92 |
| direct product | C3×H(3,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9 | C92 |
| commutator | C9 | C3×C92 |
| Frattini, cosocle | C32×C9 | C33 |
| socle | C32 | #6855 |
| prime radical | C34 | H(3,𝔽3) |
| LCS | G ▷ C9 ▷ C1 | |
| UCS | C1 ◁ C3×C9 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
638 conjugacy classes of subgroups.
| minimal degree | μ(G) = 84 |
| transitive degree | μt(G) = 243 |
315 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×H(3,ℤ/9), C9×H(3,ℤ/9), #72270990 |
| maximal normal subgroup of | C32×H(3,ℤ/9), C9×H(3,ℤ/9), #72270990 |
| maximal quotient of | C32×H(3,ℤ/9), C9×H(3,ℤ/9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 4076);