Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C5×M16 ⋊ C4 |
| Sylow | C5 ⋊ #1757 |
284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 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=e,b^2=f,c^2=e,e^2=g,b^a=bd,f^a=fg,d^b=dg,h^b=h^2,h^c=h^4,h^f=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13013691, #13013696, #13025748, … |
| maximal normal subgroup of | #13013691, #13013696, #13025748, … |
| maximal quotient of | #13016761, #13016764, #13016767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6846);