Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C5×C22⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ C22⋊#95 |
1088 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 202 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=f,b^2=g,b^a=bd,c^a=ce,h^b=h^2,h^g=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13013625, #13021742, #13021743, … |
| maximal normal subgroup of | #13013625, #13021742, #13021743, … |
| maximal quotient of | (C2×AGL(1,𝔽5))⋊#95, #13014608, #13014611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6334);