Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#430 ⋊ C2 |
| Sylow | C5 ⋊ #2091 |
222 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=de,d^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,h^c=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #12012623, #12012628, #12012633, … |
| maximal normal subgroup of | #12012623, #12012628, #12012633, … |
| maximal quotient of | #12004268, #12004272, #12004274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3604);