Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C218 |
| direct product | C23×#1790 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | #120 |
| commutator | C23 | C25×C4 |
| Frattini, cosocle | C24 | C26 |
| prime radical | C24×H(5,𝔽2) | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ C27 ◁ G | |
| LECS | G ▷ C24 ▷ C2 ▷ C1 | |
261469 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#394066, C22×#498931, C22×#494600 |
| maximal normal subgroup of | C22×#394066, C22×#498931, C22×#494600 |
| maximal quotient of | C23×#12753, #72251230, C2×#72251110 |
Past the SmallGroups library coverage — no SmallGroups id.