Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #1788 |
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^4,d^b=dg,h^b=h^4118 conjugacy classes — view the full character table.
| maximal subgroup of | #11991486, #11991491, #11991500, … |
| maximal normal subgroup of | #11991486, #11991491, #11991500, … |
| maximal quotient of | #11990677, #11990690, #11990751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2835);