Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#443 ⋊ C2 |
| Sylow | C5 ⋊ #2179 |
144 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^4,d^b=df,f^b=fg88 conjugacy classes — view the full character table.
| maximal subgroup of | #12011187, #12011188, D5×#2179, … |
| maximal normal subgroup of | #12011187, #12011188, D5×#2179, … |
| maximal quotient of | #12011037, #12011039, #12011044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3797);