Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C213 |
| direct product | C2×C3×#32898 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C25×C3 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ C26×C3 ◁ G | |
39956 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
294 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.