Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C256 (order 512) · Inn(G) = C1 · Out(G) = C2×C256 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C1024 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C512 | C2 |
| socle, prime radical | C2 | C512 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C512 ▷ C256 ▷ C128 ▷ C64 ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
11 conjugacy classes of subgroups.
1024 conjugacy classes. The character table is too large to display.
| Frattini subgroup of | D14336, Dic7168, Dic11264, … |
| maximal subgroup of | C2048, C2×C1024, C3×C1024, … |
| maximal normal subgroup of | C2048, C2×C1024, C3×C1024, … |
| maximal quotient of | C2048, C2×C1024, C3×C1024, … |
Past the SmallGroups library coverage — no SmallGroups id.