Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #10624562 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C36 |
| direct product | C3×#10624566 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C34 | C33 |
| commutator, Frattini, cosocle | C33 | C34 |
| prime radical | C35 | C32 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C34 ◁ G | |
| LECS | G ▷ C33 ▷ C1 | |
1646 conjugacy classes of subgroups; only the 494 normal subgroups are shown.
This group has 1646 conjugacy classes of subgroups — too many to draw. Only its 494 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 729 |
315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 6018);