Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #14550989 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3 | #10624599 |
| commutator, Frattini, cosocle | C34 | C33 |
| LCS | G ▷ C34 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3 ◁ C33 ◁ C35 ◁ G | |
| LECS | G ▷ C34 ▷ C33 ▷ C3 ▷ C1 | |
486 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
3^7|a^3=f,b^3=e^2,b^a=bd,c^a=ce,d^a=de,e^a=eg,d^b=df,f^b=fg^291 conjugacy classes — view the full character table.
| maximal subgroup of | #72265138 |
| maximal normal subgroup of | #72265138 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 4848);