Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #2076 |
256 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 85 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=e,c^2=dg,e^2=g,b^a=bd,c^a=ce,c^b=cf,e^c=eg,h^c=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #11985975, #11985977, #11985999, … |
| maximal normal subgroup of | #11985975, #11985977, #11985999, … |
| maximal quotient of | #12004005, #12004015, #12004039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2814);