Finite Group DatabasebetaFinite Group Databasebeta| order | 5120 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C4×C256 (order 2048) · Inn(G) = C1 · Out(G) = C2×C4×C256 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C5120 |
| abelian | C5×C1024 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C512 | C2×C5 |
| socle, prime radical | C2×C5 | C512 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
22 conjugacy classes of subgroups.
5120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C2048, C2×C5×C1024, C3×C5×C1024, … |
| maximal normal subgroup of | C5×C2048, C2×C5×C1024, C3×C5×C1024, … |
| maximal quotient of | C5×C2048, C2×C5×C1024, C3×C5×C1024, … |
Past the SmallGroups library coverage — no SmallGroups id.