Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C22⋊C16 ⋊ C2 |
| Sylow | C5 ⋊ #1314 |
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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=d,d^2=f,f^2=g,b^a=bc,c^a=ce,d^b=de,h^b=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1314, C2×#10598013, #12008360, … |
| maximal normal subgroup of | D5×#1314, C2×#10598013, #12008360, … |
| maximal quotient of | #11985918, #11985920, #11985922, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 95);