Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#525 ⋊ C2 |
| Sylow | C5 ⋊ #3050 |
520 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 149 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|b^2=e,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^b=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | #12106073, #12106074, #12106084, … |
| maximal normal subgroup of | #12106073, #12106074, #12106084, … |
| maximal quotient of | #12081539, #12081567, #12081607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16735);