Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | D3×#52163 |
| Fitting | C3×#52163 ⋊ C2 |
| Sylow | C3 ⋊ C2×#52163 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C24×D3 |
| commutator, socle, cosocle | C23×C3 | C26 |
| Frattini | C23 | C25×D3 |
| Fitting | C3×#52163 | C2 |
| hypercenter | #52163 | D3 |
| hypocenter | C3 | C2×#52163 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C4 ◁ #52163 | |
21308 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#498885, D3×#147782, D3×#7837029, … |
| maximal normal subgroup of | D3×#498885, D3×#147782, D3×#7837029, … |
| maximal quotient of | D3×#850465, D3×#609884 |
Past the SmallGroups library coverage — no SmallGroups id.