Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C5 ⋊ C8×C4⋊C4 |
296 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 165 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=e,b^2=f,c^2=de,e^2=g,b^a=bd,h^a=h^4,h^b=h^4,h^c=h^4160 conjugacy classes — view the full character table.
| maximal subgroup of | #11990061, #11990067, #11990068, … |
| maximal normal subgroup of | #11990061, #11990067, #11990068, … |
| maximal quotient of | C4⋊C8×#168, #11990432, #11990449, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3340);