Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#117 ⋊ C4 |
| Sylow | C5 ⋊ C2×#339 |
488 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^b=h^2,h^c=h^4,h^f=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#339, #13021586, #13021603, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#339, #13021586, #13021603, … |
| maximal quotient of | #13015346, #13015354, #13015362, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6454);