Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | D3×#36152 |
| Fitting | C3×#36152 ⋊ C2 |
| Sylow | C3 ⋊ C2×#36152 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C25×D3 |
| commutator, socle, cosocle | C23×C3 | C26 |
| Fitting | C3×#36152 | C2 |
| hypercenter | #36152 | D3 |
| hypocenter | C3 | C2×#36152 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #36152 | |
73296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#7630939, D3×#7684106, D3×#6595772, … |
| maximal normal subgroup of | D3×#7630939, D3×#7684106, D3×#6595772, … |
| maximal quotient of | D3×#846041, D3×#1260433, D3×#1420724, … |
Past the SmallGroups library coverage — no SmallGroups id.