Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C5×#343 ⋊ C2 |
| Sylow | C5 ⋊ C4×#100 |
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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=e,b^2=f,c^2=e,f^2=g,b^a=bd,f^a=fg,d^b=dg,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #12009661, #12009663, #12009671, … |
| maximal normal subgroup of | #12009661, #12009663, #12009671, … |
| maximal quotient of | #11989801, #11989809, #11989822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1847);