Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×C4⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ #1823 |
344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,e^c=eg,h^f=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | #13017638, #13017639, #13017640, … |
| maximal normal subgroup of | #13017638, #13017639, #13017640, … |
| maximal quotient of | #13018514, #13018515, #13018516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6364);