Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C5×H(3,ℤ/4) ⋊ C2 |
| Sylow | C5 ⋊ #1812 |
260 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 81 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=f,b^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^b=h^4,f^c=fg,h^c=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #12010287, #12010289, #12010292, … |
| maximal normal subgroup of | #12010287, #12010289, #12010292, … |
| maximal quotient of | #11992160, #11992164, #11992168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1585);