Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#117 ⋊ C4 |
| Sylow | C5 ⋊ #1827 |
262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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=f,c^2=d,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,f^b=fg,h^b=h^4,f^c=fg,h^f=h^452 conjugacy classes — view the full character table.
| maximal subgroup of | #13026191, #13026193, #13026195, … |
| maximal normal subgroup of | #13026191, #13026193, #13026195, … |
| maximal quotient of | #13018583, #13018584, #13018587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6459);