Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×#555 ⋊ C2 |
| Sylow | C5 ⋊ #3341 |
364 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 123 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=e,b^2=g,c^2=eg,d^2=g,f^2=g,b^a=beg,c^a=cf,f^a=fg,h^a=h^4,d^b=deg,f^c=fg85 conjugacy classes — view the full character table.
| maximal subgroup of | #12088940, #12088941, #12088947, … |
| maximal normal subgroup of | #12088940, #12088941, #12088947, … |
| maximal quotient of | #12115560, #12115566, #12116961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17460);