Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C5×Q16 ⋊ C2 |
| Sylow | C5 ⋊ #3011 |
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 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) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,d^c=dg,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #12130829, #12130831, #12136715, … |
| maximal normal subgroup of | #12130829, #12130831, #12136715, … |
| maximal quotient of | #12072489, #12072577, #12072665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17697);