Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #1870 |
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=df,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^c=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1870, C2×#10600751, #12100432, … |
| maximal normal subgroup of | D5×#1870, C2×#10600751, #12100432, … |
| maximal quotient of | #11993838, #11993843, #11993848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2833);