Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #2280 |
1088 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 341 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=g,d^2=e,b^a=be,c^a=cf,h^a=h^4184 conjugacy classes — view the full character table.
| maximal subgroup of | #11988955, #11988956, #11988963, … |
| maximal normal subgroup of | #11988955, #11988956, #11988963, … |
| maximal quotient of | #12020401, #12020416, C4×#65536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17840);