Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #2108 |
184 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 114 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=d,b^2=e,d^2=f,f^2=g,h^a=h^2,c^b=cg,h^d=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | #13025416, #13025660, #13025745, … |
| maximal normal subgroup of | #13025416, #13025660, #13025745, … |
| maximal quotient of | #13022965, #13022974, #13023015, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6448);