Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C35 · Schur multiplier (H2) = C312 |
| direct product | C3×H(3,𝔽9) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C33 | C34 |
| commutator, Frattini, cosocle | C32 | C35 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33 ◁ G | |
| LECS | G ▷ C32 ▷ C1 | |
7670 conjugacy classes of subgroups.
| transitive degree | μt(G) = 243 |
267 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 9109);