Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | AGL(1,ℤ/8)×B(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D4×#120 |
| commutator, Frattini, cosocle | C23×C4 | C26 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
At least 10562 conjugacy classes of subgroups; only the 4542 normal subgroups are shown.
176 conjugacy classes — view the full character table.
| maximal quotient of | #442×B(4,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id.