Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#327 ⋊ C2 |
| Sylow | C5 ⋊ #1616 |
246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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=fg,c^2=g,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^4,d^b=df,e^b=eg,d^c=dg,h^c=h^461 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1616, C2×#10599092, #12071556, … |
| maximal normal subgroup of | D5×#1616, C2×#10599092, #12071556, … |
| maximal quotient of | #11988358, #11988359, #11988386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1174);