Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C9 · Schur multiplier (H2) = C35 |
| direct product | C3×#10624706 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C9 | C33 |
| commutator | C32 | C33×C9 |
| Frattini, cosocle | C3×C9 | C34 |
| socle | C33 | C32×C9 |
| prime radical | C34 | C3×C9 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C9 ◁ G | |
| LECS | G ▷ C3×C9 ▷ C3 ▷ C1 | |
1016 conjugacy classes of subgroups.
| transitive degree | μt(G) = 729 |
459 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 8004);