Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×#460 ⋊ C2 |
| Sylow | C5 ⋊ #3216 |
390 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 113 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=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,h^b=h^4,f^c=fg,h^d=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #12076175, #12076178, #12076197, … |
| maximal normal subgroup of | #12076175, #12076178, #12076197, … |
| maximal quotient of | #12108644, #12109059, #12109870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 14202);