Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C512 (order 1024) · Inn(G) = C1 · Out(G) = C2×C512 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C2048 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C1024 | C2 |
| socle, prime radical | C2 | C1024 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C1024 ▷ C512 ▷ C256 ▷ C128 ▷ C64 ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
12 conjugacy classes of subgroups.
2048 conjugacy classes. The character table is too large to display.
| Frattini subgroup of | Dic10240, D20480, Dic14336, … |
| maximal subgroup of | C4096, C2×C2048, C3×C2048, … |
| maximal normal subgroup of | C4096, C2×C2048, C3×C2048, … |
| maximal quotient of | C4096, C2×C2048, C3×C2048, … |
Past the SmallGroups library coverage — no SmallGroups id.