Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C5×#41 ⋊ C4 |
| Sylow | C5 ⋊ #2341 |
872 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 214 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,d^2=e,b^a=be,c^a=cf,h^a=h^2,d^b=de,h^g=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #13020226, #13020227, #13020234, … |
| maximal normal subgroup of | #13020226, #13020227, #13020234, … |
| maximal quotient of | #13028000, Q8×(C2×AGL(1,𝔽5))⋊C4, #13028036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19640);