Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C5×#339 ⋊ C2 |
| Sylow | C5 ⋊ #1764 |
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 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) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^c=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1764, C2×#10599532, #12097143, … |
| maximal normal subgroup of | D5×#1764, C2×#10599532, #12097143, … |
| maximal quotient of | #11989971, #11989981, #11989988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1614);