Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4×C5×D4 ⋊ C2 |
| Sylow | C5 ⋊ #3100 |
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^4,f^c=fg118 conjugacy classes — view the full character table.
| maximal subgroup of | #11994157, #11994159, #11994490, … |
| maximal normal subgroup of | #11994157, #11994159, #11994490, … |
| maximal quotient of | #12099298, #12102228, #12104141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16121);