Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #14546205 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C33 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C32 | #6856 |
| commutator, Frattini, cosocle | C33×C9 | C32 |
| prime radical | #10624732 | C3 |
| LCS | G ▷ C33×C9 ▷ C34 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32 ◁ C34 ◁ C33×C9 ◁ G | |
| LECS | G ▷ C33×C9 ▷ C34 ▷ C32 ▷ C1 | |
195 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
3^7|a^3=fg,c^3=f^2,b^a=bc,c^a=cd,d^a=df,e^a=eg,c^b=ce,d^b=dg,e^b=ef91 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 68);