Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C33 · Schur multiplier (H2) = C24×C32 |
| direct product | C3×3−1+2×#120 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C32 | C23×C32 |
| commutator, Frattini, cosocle | C22×C3 | C23×C33 |
| prime radical | C33×#120 | C3 |
| LCS | G ▷ C22×C3 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ G | |
2470 conjugacy classes of subgroups.
462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #120×#6900, #120×C3⋊AGL(1,ℤ/9), C3×#10588712⋊C3, … |
| maximal normal subgroup of | #120×#6900, #120×C3⋊AGL(1,ℤ/9), C3×#10588712⋊C3, … |
| maximal quotient of | #120×#6900 |
Past the SmallGroups library coverage — no SmallGroups id.