Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #10624474 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C34 |
| direct product | C3×#10624475 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32 | #6856 |
| commutator, Frattini, cosocle | C34 | C33 |
| prime radical | C3×C32⋊H(3,𝔽3) | C3 |
| LCS | G ▷ C34 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32 ◁ C34 ◁ C35 ◁ G | |
| LECS | G ▷ C34 ▷ C33 ▷ C3 ▷ C1 | |
872 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 81 |
123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 4677);