Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #14551735 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C34 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3 | #10624773 |
| commutator, Frattini, cosocle | C34 | C33 |
| prime radical | #10624880 | C3 |
| LCS | G ▷ C34 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3 ◁ C33 ◁ C32×H(3,𝔽3) ◁ G | |
| LECS | G ▷ C34 ▷ C32 ▷ C3 ▷ C1 | |
395 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
3^7|a^3=d,b^a=bd,c^a=ce,e^a=ef,f^a=fg,c^b=cf^2,e^b=eg,d^c=dg^2,e^c=eg59 conjugacy classes — view the full character table.
| Fitting subgroup of | #72277708 |
| maximal subgroup of | #72265133, #72265293, #72265301, … |
| maximal normal subgroup of | #72265133, #72265293, #72265301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 5594);