Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#536 ⋊ C2 |
| Sylow | C5 ⋊ #3042 |
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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|a^2=g,b^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,f^c=fg,h^c=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #12136689, #12136692, #12147176, … |
| maximal normal subgroup of | #12136689, #12136692, #12147176, … |
| maximal quotient of | #12084514, #12084523, #12084532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17218);