Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×C22⋊C16 ⋊ C2 |
| Sylow | C5 ⋊ #2113 |
228 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 79 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=e,e^2=f,f^2=g,b^a=bd,c^b=cg,h^c=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2113, C2×#10599900, #12251975, … |
| maximal normal subgroup of | D5×#2113, C2×#10599900, #12251975, … |
| maximal quotient of | #12008363, #12008435, #12008503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1982);