Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | AGL(1,ℤ/8)×#442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D42 |
| commutator | C42 | C25×C4 |
| Frattini, cosocle | C2×C42 | C26 |
| prime radical | C2×D8×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×C43 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
At least 7168 conjugacy classes of subgroups; only the 6934 normal subgroups are shown.
242 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×AGL(1,ℤ/16) |
| maximal normal subgroup of | AGL(1,ℤ/8)×AGL(1,ℤ/16) |
| maximal quotient of | AGL(1,ℤ/8)×AGL(1,ℤ/16) |
| automorphism group of | #33856 |
Past the SmallGroups library coverage — no SmallGroups id.