Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C5×M32 ⋊ C2 |
| Sylow | C5 ⋊ #2220 |
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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|b^2=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^4,c^b=cg106 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2220, C2×#10602237, #12253765, … |
| maximal normal subgroup of | D5×#2220, C2×#10602237, #12253765, … |
| maximal quotient of | #12013533, #12013584, #12013652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4319);