Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C4 · Schur multiplier (H2) = C214 |
| direct product | C3×C4×#3498 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3×C4 | C25 |
| commutator | C22 | C25×C3×C4 |
| Frattini, cosocle | C23 | C26×C3 |
| socle | C23×C3 | C26 |
| prime radical | C2×C3×#3498 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4 ◁ G | |
24948 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
528 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.