Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C42 · Schur multiplier (H2) = C213×C4 |
| direct product | C4×#60176 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D4 |
| commutator | C4 | C24×C42 |
| Frattini, cosocle | C22×C4 | C26 |
| socle | C23 | C24×D4 |
| prime radical | C22×#576 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C42×#41 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
25341 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
328 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.