Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×#99 ⋊ C2 |
| Sylow | C5 ⋊ #2121 |
280 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=e,b^a=bd,d^a=df,f^a=fg,c^b=cg,e^b=ef,h^b=h^4,e^d=eg67 conjugacy classes — view the full character table.
| maximal subgroup of | #12014824, #12014825, #12014828, … |
| maximal normal subgroup of | #12014824, #12014825, #12014828, … |
| maximal quotient of | #12008388, #12008477, #12008558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2890);