Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C93 · Schur multiplier (H2) = C3×C92 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center | C32×C27 | C32 |
| commutator | C3 | C93 |
| Frattini, cosocle | C32×C9 | C33 |
| socle, prime radical | C33 | C32×C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C27 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
539 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2187 |
Polycyclic presentation:
3^7|a^3=d,b^3=e,c^3=f,d^3=g,c^b=cg891 conjugacy classes — view the full character table.
| Frattini subgroup of | H(3,ℤ/27) |
| maximal subgroup of | #72228248 |
| maximal normal subgroup of | #72228248 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 4072);