Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(5,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C35 · Schur multiplier (H2) = C310 |
| unambiguous semidirect product | C32⋊H(5,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C32 | C35 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32 ◁ G | |
| LECS | G ▷ C32 ▷ C1 | |
9305 conjugacy classes of subgroups.
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
3^7|b^a=bf,c^a=cg,e^d=ef315 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 9110);