Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #2031 |
244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^4,c^b=cf,d^c=dg,e^c=eg,f^c=fg82 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2031, C2×#10601161, #12126728, … |
| maximal normal subgroup of | D5×#2031, C2×#10601161, #12126728, … |
| maximal quotient of | #12002388, #12002393, #12002398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3243);