Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C5×2−1+4 ⋊ C2 |
| Sylow | C5 ⋊ #3586 |
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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|b^2=g,f^2=g,b^a=bf,e^a=eg,f^a=fg,h^a=h^4,f^b=fg,d^c=dg109 conjugacy classes — view the full character table.
| maximal subgroup of | #12130605, #12130606, #12130627, … |
| maximal normal subgroup of | #12130605, #12130606, #12130627, … |
| maximal quotient of | #12962877, #12962883, #12962984, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21270);