Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×#497 ⋊ C2 |
| Sylow | C5 ⋊ #3222 |
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^c=h^4,h^d=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | #12019693, D5×#3222, C2×#10613609, … |
| maximal normal subgroup of | #12019693, D5×#3222, C2×#10613609, … |
| maximal quotient of | #12108669, #12109099, #12109887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15691);