Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C2×#11233666 |
| Fitting | C22×C3×D42 ⋊ C2 |
| Sylow | C3 ⋊ C2×#45355 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C24×D3 |
| commutator, cosocle | C23×C3 | C26 |
| Frattini | C23 | C25×D3 |
| Fitting | C22×C3×D42 | C2 |
| socle | C24×C3 | C25 |
| hypercenter | C22×D42 | D3 |
| hypocenter | C3 | C2×#45355 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C22×D42 | |
34996 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#45355, #72255403, #72270046, … |
| maximal normal subgroup of | C2×D3×#45355, #72255403, #72270046, … |
Past the SmallGroups library coverage — no SmallGroups id.