Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #10624562 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C311 |
| direct product | C3×#10624562 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C34 | C33 |
| commutator, Frattini, cosocle | C33 | C34 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C34 ◁ G | |
| LECS | G ▷ C33 ▷ C1 | |
14228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 729 |
315 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72264819, #72264849, #72264866, … |
| maximal normal subgroup of | #72264819, #72264849, #72264866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 6010);