Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×#72292717 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #187819 |
| commutator | C2×C42 | C24×C4 |
| Frattini, cosocle | C4×M16 | C25 |
| prime radical | C2×#10575880 | C2 |
| LCS | G ▷ C2×C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C2×#2873 ◁ G | |
| LECS | G ▷ C4×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
34942 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
140 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.