Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4 |
| direct product | C2×#356055 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22⋊C42 |
| commutator | C23 | C23×C42 |
| Frattini, cosocle | C25 | C25 |
| prime radical | C23×H(5,𝔽2) | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C26 ◁ G | |
| LECS | G ▷ C25 ▷ C2 ▷ C1 | |
20021 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
202 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.