Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C213 |
| direct product | C4×#511771 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×B(4,𝔽2) |
| commutator | C22×D4 | C24×C4 |
| Frattini, cosocle | C23×D4 | C25 |
| socle | C23 | C22×B(4,𝔽2) |
| prime radical | C2×#511771 | C2 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ C23×C4×D4 ◁ G | |
| LECS | G ▷ C23×D4 ▷ C22 ▷ C2 ▷ C1 | |
113359 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
260 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.