Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C216×C4 |
| direct product | C22×#245233 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | #2403 |
| commutator, Frattini, cosocle | C25 | C26 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C27 ◁ G | |
| LECS | G ▷ C25 ▷ C22 ▷ C1 | |
338144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
224 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.