Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C216 |
| direct product | C2×#67×#120 |
| Fitting | C23×C3×#120 ⋊ C2 |
| Sylow | C3 ⋊ C2×D4×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C24×D3 |
| commutator, cosocle | C23×C3 | C26 |
| Frattini | C23 | C25×D3 |
| Fitting | C23×C3×#120 | C2 |
| socle | C24×C3 | C25 |
| hypercenter | C23×#120 | D3 |
| hypocenter | C3 | C2×D4×#120 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C23×#120 | |
82404 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×D4×#120, #72271015, #72271039, … |
| maximal normal subgroup of | C2×D3×D4×#120, #72271015, #72271039, … |
Past the SmallGroups library coverage — no SmallGroups id.