Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C22×C5×Q8 ⋊ C4 |
| Sylow | C5 ⋊ #2310 |
784 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 210 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,c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^2,c^b=ce,h^g=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13020442, #13020443, #13020450, … |
| maximal normal subgroup of | #13020442, #13020443, #13020450, … |
| maximal quotient of | #13027946, #13027969, #13027986, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19609);