Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #14546335 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3 | #10624462 |
| commutator | C27 | C3×C27 |
| Frattini, cosocle | #6864 | C32 |
| prime radical | C32 | #6875 |
| LCS | G ▷ C27 ▷ C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3 ◁ C3×C9 ◁ #6864 ◁ G | |
| LECS | G ▷ #6864 ▷ C3×C9 ▷ C3 ▷ C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
3^7|a^3=d,b^3=c,c^3=e,d^3=f,e^3=g,b^a=bc,c^a=ce,e^a=eg,d^b=de^2,f^b=fg^2,d^c=dg^2107 conjugacy classes — view the full character table.
| maximal subgroup of | #72221799, C2×#14546335 |
| maximal normal subgroup of | #72221799, C2×#14546335 |
| maximal quotient of | C2×#14546335, #72277430 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 194);