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 ⋊ #2158 |
152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 152 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,b^2=df,c^2=g,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,h^b=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | #12014688, #12014690, #12014693, … |
| maximal normal subgroup of | #12014688, #12014690, #12014693, … |
| maximal quotient of | #12010883, #12010947, #12010988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3523);