Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×#529 ⋊ C2 |
| Sylow | C5 ⋊ #3211 |
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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|b^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,f^c=fg,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #11995787, #11995789, #12073318, … |
| maximal normal subgroup of | #11995787, #11995789, #12073318, … |
| maximal quotient of | #12108621, #12108993, #12109826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16957);