Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#529 ⋊ C2 |
| Sylow | C5 ⋊ #3114 |
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^c=dg,f^c=fg,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #11997408, #11997410, #12071886, … |
| maximal normal subgroup of | #11997408, #11997410, #12071886, … |
| maximal quotient of | #12099347, #12102310, #12102325, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16956);