Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
| direct product | C2×AGL(1,ℤ/8)2 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D42 |
| commutator, Frattini, cosocle | C42 | C27 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
At least 7842 conjugacy classes of subgroups; only the 35072 normal subgroups are shown.
242 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.