Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1998 |
228 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=deg,c^2=efg,e^2=g,f^2=g,b^a=bd,c^a=cef,d^a=dg,h^a=h^2,d^b=dg,e^b=eg,f^b=fg,h^b=h^3,h^e=h^4,h^f=h^452 conjugacy classes — view the full character table.
| maximal subgroup of | #13017904, #13017905, #13017906, … |
| maximal normal subgroup of | #13017904, #13017905, #13017906, … |
| maximal quotient of | #13021458, #13021459, #13021460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6423);