Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | AGL(1,ℤ/8)×#360 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D4×#102 |
| commutator | C4×C8 | C24×C4 |
| Frattini, cosocle | C2×C4×C8 | C25 |
| prime radical | #135×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C42 ◁ C2×C8×AGL(1,ℤ/8) ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
At least 6667 conjugacy classes of subgroups; only the 1562 normal subgroups are shown.
176 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) |
Past the SmallGroups library coverage — no SmallGroups id.