Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C4 · Schur multiplier (H2) = C227 |
| direct product | C23×C4×#546 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C4 | C24 |
| commutator | C22 | C27×C4 |
| Frattini, cosocle | C23 | C28 |
| prime radical | C24×#546 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
2138328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.