Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C9 · Schur multiplier (H2) = C29 |
| direct product | C9×#32898 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C9 | C2×#120 |
| commutator | C24 | C24×C9 |
| Frattini, cosocle | C24×C3 | C24×C3 |
| socle | C22×C3 | C2×C3×#120 |
| prime radical | C3×#32898 | C3 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C9 ◁ C25×C9 ◁ G | |
6540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
441 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.