Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C5×C22⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ #1439 |
780 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=d,b^a=bd,c^a=ce,h^a=h^2,c^b=cf,h^g=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13013832, #13013834, #13017710, … |
| maximal normal subgroup of | #13013832, #13013834, #13017710, … |
| maximal quotient of | #13014608, #13014609, #13014611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6336);