Finite Group DatabasebetaFinite Group Databasebeta| order | 4640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C42×C7×C8 (order 1792) · Inn(G) = C1 · Out(G) = C2×C42×C7×C8 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C4640 |
| abelian | C5×C29×C32 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16 | C2×C5×C29 |
| socle, prime radical | C2×C5×C29 | C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
24 conjugacy classes of subgroups.
4640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C29×C64, C2×C5×C29×C32, C3×C5×C29×C32, … |
| maximal normal subgroup of | C5×C29×C64, C2×C5×C29×C32, C3×C5×C29×C32, … |
| maximal quotient of | C5×C29×C64, C2×C5×C29×C32, C3×C5×C29×C32, … |
Past the SmallGroups library coverage — no SmallGroups id.