Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(7,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C36 · Schur multiplier (H2) = C314 |
| extraspecial | 3−1+6 |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C3 | C36 |
| prime radical | C3×H(5,𝔽3) | C3 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3 ◁ G | |
| LECS | G ▷ C3 ▷ C1 | |
57194 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
3^7|a^3=g,b^a=bg,d^c=dg,f^e=fg731 conjugacy classes — view the full character table.
| maximal subgroup of | C3×3−1+6, #72290071 |
| maximal normal subgroup of | C3×3−1+6, #72290071 |
| maximal quotient of | C3×3−1+6 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 9309);