Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ #3044 |
458 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 133 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=g,b^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^4,d^b=dg,h^b=h^4,f^c=fg,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #12136713, #12136720, #12147198, … |
| maximal normal subgroup of | #12136713, #12136720, #12147198, … |
| maximal quotient of | #12084637, #12084646, #12084655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12678);