Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ #2319 |
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 162 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,d^2=f,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 | #13020132, #13020133, #13020136, … |
| maximal normal subgroup of | #13020132, #13020133, #13020136, … |
| maximal quotient of | #13027955, #13027963, #13027967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19258);