Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C220 |
| direct product | C23×D4×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C4 | C24 |
| commutator | C22 | C26×C4 |
| Frattini, cosocle | C2×C4 | C27 |
| socle | C25 | C23×C4 |
| prime radical | C25×D4 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
135245 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D4×AGL(1,ℤ/8) |
| maximal normal subgroup of | C23×D4×AGL(1,ℤ/8) |
| maximal quotient of | C22×#6373373 |
Past the SmallGroups library coverage — no SmallGroups id.