Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×#100 ⋊ C2 |
| Sylow | C5 ⋊ #2019 |
362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^4,c^b=cf,d^b=dg,f^b=fg,h^b=h^4,d^c=dg,e^c=eg,f^c=fg70 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2019, C2×#10600884, #12126502, … |
| maximal normal subgroup of | D5×#2019, C2×#10600884, #12126502, … |
| maximal quotient of | #11999907, #11999924, #11999974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2966);