Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C92 · Schur multiplier (H2) = C34×C92 |
| direct product | C3×#10624544 |
| subgroup | G/H | |
|---|---|---|
| center | C33×C9 | C32 |
| commutator | C3 | C32×C92 |
| Frattini, cosocle | C33 | C34 |
| socle, prime radical | C34 | C33 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C33×C9 ◁ G | |
| LECS | G ▷ C33 ▷ C1 | |
1898 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2187 |
891 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72271082 |
| maximal normal subgroup of | #72271082 |
| maximal quotient of | C3×C9×#6855 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 5873);