Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2960 |
364 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 166 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=e,c^2=ef,f^2=g,b^a=be,d^a=dg,h^a=h^2,h^b=h^4,h^c=h^3,h^d=h^4,h^f=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #13017141, #13017150, #13017160, … |
| maximal normal subgroup of | #13017141, #13017150, #13017160, … |
| maximal quotient of | #13033514, #13033523, #13033833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19411);