Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1920 |
230 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=fg,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^4,h^b=h^4,e^c=eg94 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1920, C2×#10601351, #12101460, … |
| maximal normal subgroup of | D5×#1920, C2×#10601351, #12101460, … |
| maximal quotient of | #11997433, #11997461, #12004954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3433);