Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C3 · Schur multiplier (H2) = C219 |
| direct product | C3×#10586472 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C27 |
| commutator, Frattini, cosocle | C22 | C27×C3 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ G | |
77460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
438 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#72216366 |
| maximal normal subgroup of | C3×#72216366 |
Past the SmallGroups library coverage — no SmallGroups id.